tag:blogger.com,1999:blog-27578090631604201992024-03-13T20:55:26.774-03:00MatheusMáthicaEste Blog tem como objetivo chamar a atenção para os fatos curiosos e interessantes da Matemática, revelando o lado divertido, desafiante e aplicado dessa ciência em diferentes contextos.MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.comBlogger1940125tag:blogger.com,1999:blog-2757809063160420199.post-54463786889810338702022-11-14T10:55:00.002-03:002022-11-14T10:55:15.063-03:00Questão 178 da prova azul do segundo dia do Enem 2020<p><b><span style="font-size: 10pt;">(Enem
2020)</span></b><span style="font-size: 10pt;">
Suponha que uma equipe de corrida de automóveis disponha de cinco tipos de pneu
(I, II, III, IV, V), em que o fator de eficiência climática EC (índice que
fornece o comportamento do pneu em uso, dependendo do clima) é apresentado:</span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">EC do pneu I: com chuva 6, sem chuva 3;<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">EC do pneu II: com chuva 7, sem chuva – 4;<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">EC do pneu III: com chuva – 2, sem chuva 10;<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">EC do pneu IV: com chuva 2, sem chuva 8;<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">EC do pneu V: com chuva – 6, sem chuva 7.<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">O coeficiente de rendimento climático (CRC)
de um pneu é calculado como a soma dos produtos dos fatores de EC, com ou sem
chuva, pelas correspondentes probabilidades de se ter tais condições
climáticas: ele é utilizado para determinar qual pneu deve ser selecionado para
uma dada corrida, escolhendo-se o pneu que apresentar o maior CRC naquele dia. No
dia de certa corrida, a probabilidade de chover era de 70% e o chefe da equipe
calculou o CRC de cada um dos cinco tipos de pneu.<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">O pneu escolhido foi<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10.0pt;">A) I.</span></b><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><span style="mso-spacerun: yes;"> </span>B) II.<span style="mso-spacerun: yes;"> </span>C) III.<span style="mso-spacerun: yes;"> </span>D) IV.<span style="mso-spacerun: yes;"> </span>E) V.<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p class="MsoNormal"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Basta observar que o coeficiente de
rendimento climático é calculado como a soma dos produtos dos fatores EC, pelas
correspondentes probabilidades de se ter tais condições climáticas.<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Probabilidade de chover: 70%<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Probabilidade de não chover: 30%<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Assim, calcularemos o CRC de cada questão.<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Para o pneu I tem se:</span></i><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"> </span><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">6 ∙
70 + 3 ∙ 30 = 420 + 90 = 510<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Para o pneu I tem se:</span></i><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"> </span><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">7 ∙
70 + (-4) ∙ 30 = 490 – 120 = 370<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Para o pneu I tem se:</span></i><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"> </span><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">-2
∙ 70 + 10 ∙ 30 = -140 + 300 = 160<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Para o pneu I tem se:</span></i><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"> </span><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">2 ∙
70 + 8 ∙ 30 = 140 + 240 = 380<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Para o pneu I tem se:</span></i><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"> <span style="mso-spacerun: yes;"> </span></span><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">-6 ∙ 70 + 7 ∙ 30 = -420 + 210 = -210<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Portanto, o pneu escolhido foi o de número
1.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-77484805955995910142022-11-14T08:18:00.004-03:002022-11-14T08:18:56.791-03:00Questão 141 da prova azul do segundo dia do Enem 2020<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem 2020) </span></b><span style="font-size: 10pt; text-align: justify;">Um hotel de 3 andares
está sendo construído. Cada andar terá 100 quartos. Os quartos serão numerados
de 100 a 399 e cada um terá seu número afixado à porta. Cada número será
composto por peças individuais, cada uma simbolizando um único algarismo.</span></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;">Qual
a quantidade mínima de peças, simbolizando o algarismo 2, necessárias para
identificar o número de todos os quartos?<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10.0pt;">A) 160</span></b><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><span style="mso-spacerun: yes;"> </span>B) 157<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>C) 130<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>D) 120<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>E) 60<o:p></o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt; mso-themecolor: text1;"><o:p> </o:p></span></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Basta listar todos os números de 100 a 199 que possuem o
algarismo 2. São eles: 102, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128,
129, 132, 142, 152, 162, 172, 182, 192. Se contarmos, são 20 vezes que usamos o
algarismo 2. De forma análoga, usamos a mesma ideia para quantidade de 300 a
399. Já de 200 a 299 temos 100 algarismos e, além dos 20 que contamos para a
quantidade que contamos nas centenas anteriores, vamos considerar que em cada
número de 200 a 299 tem um “2” no algarismo da centena. Logo,<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">De 100 a 199: 20 dígitos “2”<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">De 200 a 299: 20 + 100 = 120 dígitos “2”<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">De 300 a 399: 20 dígitos “2”<o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></i></p>
<p style="margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Portanto, tem se<span style="mso-spacerun: yes;"> </span>um total:
20+120+20=160 dígitos “2”.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-47644552832271549562022-11-13T17:07:00.004-03:002022-11-13T17:14:04.729-03:00Questão 154 da prova cinza do segundo dia do Enem PPL 2014 <p> </p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75"
coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="Imagem_x0020_24" o:spid="_x0000_s1026" type="#_x0000_t75"
alt="Representação de figura em formato de triângulo equilátero de lado com 1 m."
style='position:absolute;left:0;text-align:left;margin-left:309.35pt;
margin-top:-7.9pt;width:161.25pt;height:115.5pt;z-index:1;visibility:visible;
mso-wrap-style:square;mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;
mso-wrap-distance-right:9pt;mso-wrap-distance-bottom:0;
mso-position-horizontal:absolute;mso-position-horizontal-relative:margin;
mso-position-vertical:absolute;mso-position-vertical-relative:margin'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"
o:title="Representação de figura em formato de triângulo equilátero de lado com 1 m"/>
<w:wrap type="square" anchorx="margin" anchory="margin"/>
</v:shape><![endif]--><!--[if !vml]--><img align="left" alt="Representação de figura em formato de triângulo equilátero de lado com 1 m." height="154" hspace="12" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="Imagem_x0020_24" width="215" /><!--[endif]--><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10.0pt;">10.<span style="mso-spacerun: yes;"> </span><span style="color: black;">(Enem PPL 2014)</span></span></b><span style="color: black; font-size: 10.0pt;"> Um artista deseja pintar em um quadro uma figura na forma
de triângulo equilátero ABC de lado 1 metro. Com o objetivo de dar um efeito
diferente em sua obra, o artista traça segmentos que unem os pontos médios D, E
e F dos lados BC, AC e AB, respectivamente, colorindo um dos quatro triângulos
menores, como mostra a figura.<o:p></o:p></span></p>
<p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">Qual
é a medida da área pintada, em metros quadrados, do triângulo DEF?<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">A)
1/16<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>B) √3/16<span style="mso-spacerun: yes;">
</span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>C) 1/8<span style="mso-spacerun: yes;">
</span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>D) √3/8<span style="mso-spacerun: yes;">
</span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>E)
√3/4<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">Como D, E e F são os
pontos médios dos lados do </span></i><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;">triângulo equilátero </span></i><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">ABC, então DE = EF = DF =
0,5m. A área do triângulo equilátero DEF é encontrada aplicando a fórmula da
área do triângulo eqüilátero, ou seja:<o:p></o:p></span></i></p>
<p class="MsoNormal"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:red'><m:r>A</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:red'><m:r>T</m:r></span></i></m:sub></m:sSub></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-fareast-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:red'><m:r>e</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-fareast-font-family:"Times New Roman";
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<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-51302645519530005062022-11-13T16:42:00.003-03:002022-11-13T17:13:45.784-03:00Questão 146 da prova cinza do segundo dia do Enem PPL 2015 <p> </p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;"><o:p> </o:p></span></i></p>
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</v:shape><![endif]--><!--[if !vml]--><img align="left" alt="Tabela com fornecedores e valores de azulejos e lajotas — enunciado questão Enem 2015" height="125" hspace="12" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="Imagem_x0020_28" width="274" /><!--[endif]--><span style="font-size: 10pt;"><b style="mso-bidi-font-weight: normal;"><span style="background: white; border: 1pt none windowtext; color: black; mso-border-alt: none windowtext 0cm; padding: 0cm;">(Enem PPL 2015)</span></b><span style="background: white; border: 1pt none windowtext; color: black; mso-border-alt: none windowtext 0cm; padding: 0cm;"> O banheiro de uma escola pública, com paredes e piso em
formato retangular, medindo 5 metros de largura, 4 metros de comprimento e 3
metros de altura, precisa de revestimento no piso e nas paredes internas,
excluindo a área da porta, que mede 1 metro de largura por 2 metros de altura.
Após uma tomada de preços com cinco fornecedores, foram verificadas as
seguintes combinações de azulejos para as paredes e de lajotas para o piso, com
os preços dados em reais por metro quadrado, conforme a tabela.</span><span style="color: black;"><o:p></o:p></span></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: 1pt none windowtext; color: black; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Desejando-se efetuar a menor despesa total, deverá ser
escolhido o fornecedor:</span><span style="color: black; font-size: 10pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: 1pt none windowtext; color: black; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: 1pt none windowtext; color: black; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">A) A<span style="mso-spacerun: yes;"> </span>B) B<span style="mso-spacerun: yes;"> </span>C) C<span style="mso-spacerun: yes;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="background: white; border: 1pt none windowtext; color: red; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">D) D</span></b><span style="background: white; border: 1pt none windowtext; color: black; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><span style="mso-spacerun: yes;"> </span>E) E</span><span style="color: black; font-size: 10pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10pt;"><o:p> </o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10pt;"><o:p> </o:p></span></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">Pelas informações dadas tem-se area do piso
é A1= 5 . 4 = 20 m², área da parede interna sem a porta A2= (4+4+5+5)3= 54 m² e
área da porta A3=2.1= 2 m², portanto a área do revestimento de azulejo é A= A2-A3=54-2=72
m². Agora comparando preço a preço tem-se<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">A: 31 . 52+31.20=2232<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">B: 33 . 52+30.20=2316<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">C: 29 . 52+39.20=2288<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">D: 30 . 52+33.20=2220<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">E: 40. 52+ 29. 20=2660<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt; mso-no-proof: yes;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">Portanto, o fornecedor escolhido foi o D.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-88143032554147795032022-11-13T16:18:00.004-03:002022-11-13T17:15:03.894-03:00Questão 146 da prova cinza do segundo dia do Enem PPL 2013<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem PPL 2013)</span></b><span style="font-size: 10pt; text-align: justify;"> A logomarca de uma empresa de computação
é um quadrado, <em><span style="border: 1pt none windowtext; mso-border-alt: none windowtext 0cm; padding: 0cm;">AEFG</span></em>, com partes pintadas como
mostra a figura. Sabe-se que todos os ângulos agudos presentes na figura medem
45° e que <em><span style="border: 1pt none windowtext; mso-border-alt: none windowtext 0cm; padding: 0cm;">AB = BC = CD = DE</span></em>. A fim de
divulgar a marca entre os empregados, a gerência decidiu que fossem pintadas
logomarcas de diversos tamanhos nas portas, paredes e fachada da empresa.
Pintadas as partes cinzas de todas as logomarcas, sem desperdício e sem sobras,
já foram gastos R$ 320. O preço das tintas cinza, preta e branca é o mesmo.</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;"><o:p> </o:p></span></p><div class="separator" style="clear: both; text-align: center;"><img alt="" border="0" class="placeholder" height="240" id="ddca6af7376a" src="https://www.blogger.com/img/transparent.gif" style="background-color: #d8d8d8; background-image: url('https://fonts.gstatic.com/s/i/materialiconsextended/insert_photo/v6/grey600-24dp/1x/baseline_insert_photo_grey600_24dp.png'); background-position: 50% 50%; background-repeat: no-repeat; opacity: 0.6;" width="320" /></div><br /><p></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">Considerando
que não haja desperdício e sobras, o custo para pintar as partes pretas e o
custo para pintar as partes brancas serão, respectivamente,<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">A)
R$ 320 e R$ 640.<span style="mso-spacerun: yes;"> </span>B) R$ 640 e R$ 960.<span style="mso-spacerun: yes;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10pt;">C) R$ 960 e R$ 1280</span></b><span style="color: black; font-size: 10pt;">.<span style="mso-spacerun: yes;"> </span>D)
R$ 1280 e R$ 2240.<span style="mso-spacerun: yes;"> </span>E) R$ 2240 e R$ 2560.<o:p></o:p></span></p>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">Pelas informações dadas podemos repartir a
figura em quadrados menores, onde é possível verificar a área cinza é formada por
4 triângulos, a preta por 12 e a branca por 16, sendo todos eles congruentes,
pelo caso LAL (note que os triângulos são isósceles com um ângulo reto). Dessa
forma, para encontrar<span style="mso-spacerun: yes;"> </span>o valor gastão para
pintar a área preta e branca,<span style="mso-spacerun: yes;"> </span>basta
fazer, respectivamente,<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>4</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>320</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>12</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>p</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r> ⇒</m:r><m:r>p</m:r><m:r>=960<span
style='mso-spacerun:yes'> </span></m:r><m:r>e</m:r><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>320</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
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mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>p</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">Portanto, o custo para pintar a área preta deverá
R$960,00 e branca de R$1280,00<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-75340335057518479972022-11-13T15:38:00.003-03:002022-11-13T15:38:39.026-03:00Questão 145 da prova do segundo dia do Enem PPL 2010<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem PPL 2010)</span></b><span style="font-size: 10pt; text-align: justify;"> João tem uma loja onde fabrica e vende
moedas de chocolate com diâmetro de 4 cm e preço de R$ 1,50 a unidade. Pedro
vai a essa loja e, após comer várias moedas de chocolate, sugere ao João que
ele faça moedas com 8 cm de diâmetro e mesma espessura e cobre R$ 3 a unidade.</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">Considerando
que o preço da moeda depende apenas da quantidade de chocolate, João<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">A)
aceita a proposta de Pedro, pois, se dobra o diâmetro, o preço também deve
dobrar.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">B)
rejeita a proposta de Pedro, pois o preço correto seria R$ 12.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">C)
rejeita a proposta de Pedro, pois o preço correto seria R$ 7,50.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">D)
rejeita a proposta de Pedro, pois o preço correto seria R$ 6.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">E)
rejeita a proposta de Pedro, pois o preço correto seria R$ 4,50.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Como a moeda é circular sua a área é
encontrada pela área de um círculo (A=πr²) e o sabemos que o diâmetro equivale
a duas vezes o valor do raio (D=2r), então para diâmetro igual a 4 cm tem-se r=4/2=2
cm e, consequentemente, A=2²π=4π. Já com diâmetro igual a <span style="mso-spacerun: yes;"> </span>8 cm tem-se r=8/2=4 cm e, consequentemente, A=4²π=16π.<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Como a área da moeda aumentou 4 vezes o
preço tem que aumentar 4 vezes também, logo P= 4 x1,50 = R$6,00<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Portanto, João vai <span style="mso-spacerun: yes;"> </span>rejeita a proposta de Pedro, pois o preço
correto seria R$ 6.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-8327723974929523472022-11-13T15:13:00.003-03:002022-11-13T15:16:15.936-03:00Questão 149 da prova do segundo dia do Enem 2020 Digital<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem Digital 2020)</span></b><span style="font-size: 10pt; text-align: justify;"><img align="left" alt="Representação de logomarca, em formato de um quadrado, de empresa de computação — enunciado questão Enem 2013" height="178" hspace="12" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="Imagem_x0020_20" width="186" /> Uma empresa deseja construir um edifício
residencial de 12 pavimentos, num lote retangular de lados medindo 22 e 26 m.
Em 3 dos lados do lote serão construídos muros. A frente do prédio será sobre o
lado do lote de menor comprimento. Sabe-se que em cada pavimento 32 m<sup><span style="border: none windowtext 1.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">2</span></sup> serão destinados à área comum (hall de
entrada, elevadores e escada), e o restante da área será destinado às unidades
habitacionais. A legislação vigente exige que prédios sejam construídos
mantendo distâncias mínimas dos limites dos lotes onde se encontram. Em
obediência à legislação, o prédio ficará 5 m afastado da rua onde terá sua
entrada, 3 m de distância do muro no fundo do lote e 4 m de distância dos muros
nas laterais do lote, como mostra a figura.</span></p>
<p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">A
área total, em metro quadrado, destinada às unidades habitacionais desse
edifício será de<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="background-color: transparent; text-align: left;"><span style="color: red; font-family: "Calibri","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">A) 2640.</span></b><span style="background-color: transparent; font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%; text-align: left;"> </span><span style="color: black; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">B) 3024.<span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><span style="mso-spacerun: yes;"></span>C) 3840.<span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">D) 6480.<span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">E) 6864.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">De acordo com as informações do enunciado,
vamos encontrar a área onde o edifício residencial de 12 pavimentos
("andares") será construído. Assim, a construção do edifício terá comprimento
de C=22 – 4-4=14 m e largura de L=26-3-6=18 m. Logo, a área destinada a construção
do edifício será A=14 </span></i><span style="color: red; font-size: 10.0pt;">x <i style="mso-bidi-font-style: normal;">18 = 252 m². </i></span><!--[if gte vml 1]><v:shapetype
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</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">O objetivo da questão é calcular a área
total, em metro quadrado, destinada às unidades habitacionais dos 12 pavimentos
deste edifício.<span style="mso-spacerun: yes;"> </span>Neste momento, temos que
atentar para a seguinte informação do enunciado: "sabe-se que em cada
pavimento 32 m² serão destinados à área comum (hall de entrada, elevadores e
escada), e o restante da área será destinado às unidades habitacionais."
Dessa forma, cada pavimento terá 252 - 32<span style="mso-spacerun: yes;">
</span>= 220 m² de área destinada às unidades habitacionais. E <span style="mso-spacerun: yes;"> </span>como são 12 pavimentos, basta multiplicar 12,<span style="mso-spacerun: yes;"> </span>ou seja, área solicitada é AT=12 </span></i><span style="color: red; font-size: 10.0pt;">x<i style="mso-bidi-font-style: normal;"> 220
= 2640 m².<o:p></o:p></i></span></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-74162425853583130252022-11-13T14:56:00.002-03:002022-11-13T17:16:11.570-03:00Questão 171 da prova cinza do segundo dia do Enem PPL 2015 <p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem PPL 2015)</span></b><span style="font-size: 10pt; text-align: justify;"> O prefeito de uma cidade deseja promover
uma festa popular no parque municipal para comemorar o aniversário de fundação
do município. Sabe-se que esse parque possui formato retangular, com 120 m de
comprimento por 150 m de largura. Além disso, para segurança das pessoas
presentes no local, a polícia recomenda que a densidade média, num evento dessa
natureza, não supere quatro pessoas por metro quadrado.</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">Seguindo
as recomendações de segurança estabelecidas pela polícia, qual é o número
máximo de pessoas que poderão estar presentes na festa?<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">A)
1000<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">B) 4500<span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">C) 18.000<span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10pt;">D) 72.000</span></b><span style="color: black; font-size: 10pt;"><span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">E) 120.000<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: 1pt none windowtext; color: black; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: 1pt none windowtext; color: red; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: 1pt none windowtext; color: red; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: 1pt none windowtext; color: red; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Como são 4 pessoas por metro
quadrado, então a cada m² temos 4 pessoas. Seja P o número máximo de pessoas,
tem-se:<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: 1pt none windowtext; color: red; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: 1pt none windowtext; color: red; font-size: 10pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">P = 4 . 150 . 120 = 72.000
pessoas<o:p></o:p></span></i></p><br /><p></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-654666700984885332022-11-13T14:48:00.005-03:002022-11-13T14:49:17.025-03:00Questão 136 da prova amarelo do segundo dia do Enem PPL 2018<p> </p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75"
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</v:shape><![endif]--><!--[if !vml]--><img align="left" alt="Representação de cama elástica com contorno em formato de um hexágono regular" height="136" hspace="12" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg" v:shapes="Imagem_x0020_7" width="136" /><!--[endif]--><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10.0pt;"><span style="background: white; border: none windowtext 1.0pt; color: black; mso-border-alt: none windowtext 0cm; padding: 0cm;">(Enem PPL 2018)</span></span></b><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"> Um
brinquedo chamado pula-pula, quando visto de cima, consiste de uma cama
elástica com contorno em formato de um hexágono regular.</span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Se a área do círculo inscrito no hexágono é 3π metros
quadrados, então a área do hexágono, em metro quadrado, é: </span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><br /></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><br /></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><br /></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">A) 9 <span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><b style="background-color: transparent; text-align: left;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1pt none windowtext; color: red; font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%; padding: 0cm;">B) 6√3</span></b><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1pt none windowtext; font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%; padding: 0cm; text-align: left;"> </span><span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">C)
9√2 <span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">D) 12 <span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">E) 12</span><span style="color: black; font-size: 10.0pt;">√<span style="background: white; border: none windowtext 1.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">3</span><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Se a área do círculo é A=3π m², então <o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>r</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;mso-ascii-font-family:"Cambria Math";color:red'><m:r>²</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>π</m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r> =3</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>π</m:r><m:r>⇒</m:r><m:r>r</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:10.0pt;mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i></m:e></m:rad><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r> </m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>m</m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:105pt;height:27.75pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="37" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1025" width="140" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Cambria Math","serif"; font-size: 10.0pt; mso-hansi-font-family: "Times New Roman"; mso-omath-para: yes;"><o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Ademais, como o triângulo ABO é equilátero,
tem-se que o raio é equivalente a altura desse citado triângulo. Mas,<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-ascii-font-family:
"Cambria Math";color:red'><m:r>h</m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:"Cambria Math";color:red'><m:r><m:rPr><m:scr
m:val="script"/><m:sty m:val="i"/></m:rPr>l</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r><m:rPr><m:scr m:val="script"/><m:sty m:val="i"/></m:rPr> </m:r></span></i><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:10.0pt;mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i></m:e></m:rad></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>2</m:r></span></i></m:den></m:f><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>⇒</m:r></span></i><m:rad><m:radPr><m:degHide m:val="on"/><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i></m:e></m:rad><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r>= </m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:"Cambria Math";color:red'><m:r><m:rPr><m:scr
m:val="script"/><m:sty m:val="i"/></m:rPr>l</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r><m:rPr><m:scr m:val="script"/><m:sty m:val="i"/></m:rPr> </m:r></span></i><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:10.0pt;mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i></m:e></m:rad></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>2</m:r></span></i></m:den></m:f><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>⇒</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;mso-ascii-font-family:"Cambria Math";color:red'><m:r><m:rPr><m:scr
m:val="script"/><m:sty m:val="i"/></m:rPr>l</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r>
=2 </m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";color:red'><m:r>m</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:159.75pt;height:39pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="52" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="213" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Aplicando a formula da área do hexágono
regular tem-se:<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>A</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>H</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i><m:sSup><m:sSupPr><span style='font-size:
10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:
"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";color:red;
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
mso-ascii-font-family:"Cambria Math";color:red'><m:r><m:rPr><m:scr
m:val="script"/><m:sty m:val="i"/></m:rPr>l</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>2</m:r></span></i></m:sup></m:sSup><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r> </m:r></span></i><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:10.0pt;mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i></m:e></m:rad></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>2</m:r></span></i></m:den></m:f><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;mso-ascii-font-family:"Cambria Math";color:red'><m:r>∙</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>2</m:r></span></i></m:e><m:sup><i style='mso-bidi-font-style:
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mso-hansi-font-family:"Times New Roman";color:red'><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
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color:red'><m:r> </m:r></span></i><m:rad><m:radPr><m:degHide m:val="on"/><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
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color:red'><m:r>3</m:r></span></i></m:e></m:rad></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
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color:red'><m:r>2</m:r></span></i></m:den></m:f><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r>=6</m:r></span></i><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:10.0pt;mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red'><m:r>3</m:r></span></i></m:e></m:rad><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r> </m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>m</m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;mso-ascii-font-family:"Cambria Math";
color:red'><m:r>²</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:150pt;height:39pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png"
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<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Portanto, área solicitada é equivalente a </span></i><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r>6</m:r></span></i><m:rad><m:radPr><m:degHide
m:val="on"/><span style='font-size:10.0pt;mso-ansi-font-size:10.0pt;
mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:
"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r>3</m:r></span></i></m:e></m:rad><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red'><m:r>
</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";color:red'><m:r>m</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;mso-ascii-font-family:
"Cambria Math";color:red'><m:r>²</m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red'><m:r>.</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:33pt;height:27pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image009.png"
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</v:shape><![endif]--><!--[if !vml]--><img height="36" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image010.gif" v:shapes="_x0000_i1025" width="44" /><!--[endif]--></span><!--[endif]--><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p></o:p></span></i></b></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-19019829340309268672022-11-13T14:26:00.002-03:002022-11-13T14:26:09.745-03:00Questão 147 da prova azul do segundo dia do Enem 2019<p> </p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75"
coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
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<v:formulas>
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</v:shapetype><v:shape id="Imagem_x0020_5" o:spid="_x0000_s1026" type="#_x0000_t75"
alt="Representação de placa de sinalização de “É proibido estacionar” com marcação do diâmetro e altura"
style='position:absolute;left:0;text-align:left;margin-left:363.45pt;
margin-top:-.3pt;width:92.25pt;height:110.25pt;z-index:1;visibility:visible;
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o:title="Representação de placa de sinalização de “É proibido estacionar” com marcação do diâmetro e altura"/>
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</v:shape><![endif]--><!--[if !vml]--><img align="left" alt="Representação de placa de sinalização de “É proibido estacionar” com marcação do diâmetro e altura" height="147" hspace="12" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg" v:shapes="Imagem_x0020_5" width="123" /><!--[endif]--><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10.0pt;">3.<span style="mso-spacerun: yes;"> </span><span style="background: white; border: none windowtext 1.0pt; color: black; mso-border-alt: none windowtext 0cm; padding: 0cm;">(Enem 2019) </span></span></b><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Uma administração municipal
encomendou a pintura de dez placas de sinalização para colocar em seu pátio de
estacionamento. O profissional contratado para o serviço inicial pintará
o fundo de dez placas e cobrará um valor de acordo com a área total dessas
placas. O formato de cada placa é um círculo de diâmetro d = 40 cm,
que tangencia lados de um retângulo, sendo que o comprimento total da placa
é h = 60 cm, conforme ilustrado na figura. Use 3,14 como aproximação
para π.</span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Qual é a soma das medidas das áreas, em centímetros
quadrados, das dez placas?</span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">A) 16.628 <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">B) 22.280</span></b><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"> <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>C)
28.560<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>D) 41.120<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>E) 66.240<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Podemos decompor a área da
placa como um semicírculo de raio 20 cm e um quadrado de lado 40 cm . Logo a
área é dada por:<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>A</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>p</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red;
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;padding:0cm;
background:white'><m:r>=</m:r></span></i><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>A</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>S</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red;
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;padding:0cm;
background:white'><m:r>+</m:r></span></i><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>A</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>Q</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red;
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;padding:0cm;
background:white'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:
10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:
"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";color:red;
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;padding:
0cm;background:white;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white'><m:r>20</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white'><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>∙</m:r><m:r>π</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white'><m:r>2</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red;
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;padding:0cm;
background:white'><m:r>+</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white'><m:r>40</m:r></span></i></m:e><m:sup><i
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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background:white'><m:r>=200</m:r></span></i><i style='mso-bidi-font-style:
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color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white'><m:r>π</m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>+1600 </m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
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<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><span style="mso-spacerun: yes;"> </span>Como a questão manda usar<span style="mso-spacerun: yes;"> </span>3,14 como aproximação para π, então<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>A</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red;border:none windowtext 1.0pt;
mso-border-alt:none windowtext 0cm;padding:0cm;background:white'><m:r>p</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red;
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;padding:0cm;
background:white'><m:r>=200</m:r></span></i><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;mso-ascii-font-family:"Cambria Math";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white'><m:r>∙</m:r></span></i><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
color:red;border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;
padding:0cm;background:white'><m:r>3,14</m:r></span></i></m:e></m:d><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";color:red;
border:none windowtext 1.0pt;mso-border-alt:none windowtext 0cm;padding:0cm;
background:white'><m:r>+1600=2228 </m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
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<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><span style="mso-spacerun: yes;"> </span>Como são 10 placas, então </span></i><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red;border:none windowtext 1.0pt;mso-border-alt:
none windowtext 0cm;padding:0cm;background:white'><m:r>2228</m:r><m:r>∙</m:r><m:r>10
= 22280 </m:r><m:r>cm</m:r><m:r>²</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><!--[if !vml]--><img height="35" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1025" width="139" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">. </span></i><i style="mso-bidi-font-style: normal;"><span style="background: white; border: none windowtext 1.0pt; color: red; font-family: "Cambria Math","serif"; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; mso-omath-para: yes; padding: 0cm;"><o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-57423259176990675692022-11-13T14:14:00.001-03:002022-11-13T14:14:18.004-03:00Questão 155 da prova azul do segundo dia do Enem 2015<p> </p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></p>
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</v:shape><![endif]--><!--[if !vml]--><img align="left" alt="Representação das áreas de cobertura das antenas — enunciado questão Enem 2015" height="174" hspace="12" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="Imagem_x0020_3" width="232" /><!--[endif]--><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10.0pt;">2.<span style="mso-spacerun: yes;"> </span>(<span style="background: white; border: none windowtext 1.0pt; color: black; mso-border-alt: none windowtext 0cm; padding: 0cm;">Enem 2015)</span></span></b><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"> Uma empresa
de telefonia celular possui duas antenas que serão substituídas por uma nova,
mais potente. As áreas de cobertura das antenas que serão substituídas são
círculos de raio 2 km, cujas circunferências se tangenciam no ponto O como
mostra a figura. O ponto O indica a posição da nova antena, e sua
região de cobertura será um círculo cuja circunferência tangenciará
externamente as circunferências das áreas de cobertura menores.</span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Com a instalação da nova antena, a medida da área de
cobertura, em quilômetros quadrados, foi ampliada em </span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><b><br /></b></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;"><b style="background-color: transparent; text-align: left;"><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1pt none windowtext; color: red; font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%; padding: 0cm;">A) 8π.</span></b><span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 1pt none windowtext; font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%; padding: 0cm; text-align: left;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">B) 12 π. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">C) 16 π. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">D)
32 π. <span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">E) 64 π.</span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10.0pt;"><o:p> </o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 10.0pt;"><o:p> </o:p></span></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Temos que a área de uma circunferência é
dada pela fórmula A= πr². Como as duas circunferência tem raio 2. Logo, a área
total coberta pelas antenas antigas eram de<span style="mso-spacerun: yes;">
</span>AT=2.2².π=8π Km².<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Já a área coberta pela nova antena tem o
raio do tamanho do diâmetro área de qualquer uma das duas circunferência, ou
seja, R=2.2=4 Km. Assim, a nova área equivale a An=4² π.=16 π Km². Logo, ampliação
é dado por a= 16π-8π=8π Km² .<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Portanto, a área aumentou de 8π.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-47558180608449009772022-11-13T13:43:00.005-03:002022-11-13T13:43:51.626-03:00Questão 143 da prova azul do segundo dia do Enem 2016<p><b style="text-align: justify;"><span style="font-size: 10.0pt;">1. <span style="background: white; border: 1pt none windowtext; padding: 0cm;">(Enem
2016) </span></span></b><span style="background: white; border: 1pt none windowtext; font-size: 10pt; padding: 0cm; text-align: justify;">Um senhor, pai de dois filhos, deseja comprar dois
terrenos, com áreas de mesma medida, um para cada filho. Um dos terrenos
visitados já está demarcado e, embora não tenha um formato convencional (como
se observa na Figura B), agradou ao filho mais velho e, por isso, foi comprado.
O filho mais novo possui um projeto arquitetônico de uma casa que quer
construir, mas, para isso, precisa de um terreno na forma retangular (como
mostrado na Figura A) cujo comprimento seja 7 m maior do que a
largura.</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
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alt="Questão ENEM - 2016 | Matemática | Áreas De Superfícies Planas | Respondida e comentada"
style='width:301.5pt;height:127.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"
o:title="Questão ENEM - 2016 | Matemática | Áreas De Superfícies Planas | Respondida e comentada"/>
</v:shape><![endif]--><!--[if !vml]--><img alt="Questão ENEM - 2016 | Matemática | Áreas De Superfícies Planas | Respondida e comentada" height="170" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="Imagem_x0020_2" width="402" /><!--[endif]--></span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">Para satisfazer o filho mais novo, esse senhor precisa
encontrar um terreno retangular cujas medidas, em metro, do comprimento e da
largura sejam iguais, respectivamente, a <o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="background: white; border: none windowtext 1.0pt; color: black; font-size: 10.0pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">A) 7,5 e 14,5. <span style="mso-spacerun: yes;"> </span>B) 9,0 e 16,0. <span style="mso-spacerun: yes;"> </span>C) 9,39,3 e 16,3. <span style="mso-spacerun: yes;"> </span>D) 10,0 e 17,0. <span style="mso-spacerun: yes;"> </span>E) 13,5 e 20,5.</span><span style="color: black; font-size: 10.0pt;"><o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Primeiramente, dividimos a figura B em dois triângulos B1 e B2, um
com altura de 21 m e base de 3 m e outro com altura e base medindo 15 m.<o:p></o:p></span></i></p>
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Imagem_x0020_5" o:spid="_x0000_i1025"
type="#_x0000_t75" style='width:150.75pt;height:124.5pt;visibility:visible;
mso-wrap-style:square'>
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o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><img height="166" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.jpg" v:shapes="Imagem_x0020_5" width="201" /><!--[endif]--></span></i><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Assim, temos que área da figura A é igual a área da figura B = B1 +
B2<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>x</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:red'><m:r> +
7</m:r></span></i></m:e></m:d><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>15</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>∙</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:red'><m:r> +</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>21</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>∙</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
"Times New Roman";mso-bidi-font-family:"Times New Roman";color:red'><m:r>3</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:red'><m:r><span style='mso-spacerun:yes'> </span></m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";color:red'><m:r>⇒</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
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mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>x</m:r></span></i></m:e><m:sup><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>2</m:r></span></i></m:sup></m:sSup><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>+7</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-bidi-font-family:
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normal'><span style='font-size:10.0pt;font-family:"Times New Roman","serif";
color:red'><m:r>-</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
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</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>⇒</m:r><m:r>x</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";color:red'><m:r>-</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>7</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>±</m:r></span></i><m:rad><m:radPr><m:degHide m:val="on"/><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>7</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";color:red'><m:r>-</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>4</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>∙</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>∙</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>-</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>∙</m:r></span></i><i style='mso-bidi-font-style:normal'><span
style='font-size:10.0pt;font-family:"Cambria Math","serif";mso-hansi-font-family:
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
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mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";color:red'><m:r>-</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>7</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";mso-ascii-font-family:"Cambria Math";
color:red'><m:r>±</m:r></span></i><m:rad><m:radPr><m:degHide m:val="on"/><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>625</m:r></span></i></m:e></m:rad></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
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o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="37" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="571" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Cambria Math","serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-omath-para: yes;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Como o valor negativo não é válido para medida, então<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";color:red'><m:r>x</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Times New Roman","serif";color:red'><m:r>-</m:r></span></i><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>7+25</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>=9</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
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<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="33" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1025" width="98" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Cambria Math","serif"; font-size: 10.0pt; mso-bidi-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-omath-para: yes;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Assim, uma altura mede 9 m e largura 9 + 7 =16 m. Portanto, as
medidas do retângulo são 9 m e 16 m.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-78537871957221282932022-11-13T12:59:00.005-03:002022-11-13T13:12:29.571-03:00Questão 169 da prova azul do segundo dia do Enem 2014<p> <b style="text-align: justify;"><span style="font-size: 10pt;">(Enem 2014)</span></b><span style="font-size: 10pt; text-align: justify;"> A Figura 1 representa uma gravura
retangular com 8 m de comprimento e 6 m de altura.</span></p>
<p align="center" style="background: white; break-after: avoid; margin-bottom: .0001pt; margin: 0cm; page-break-after: avoid; text-align: center;"><span style="color: black; font-size: 10pt; mso-no-proof: yes;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75"
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alt="Gravura retangular com 8 m de comprimento e 6 m de altura em enunciado de questão do Enem"
style='width:289.5pt;height:235.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"
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<p align="center" class="MsoCaption" style="text-align: center;"><span color="windowtext" style="font-family: "Times New Roman","serif"; font-size: 8pt;">Figura
</span><!--[if supportFields]><span style='font-size:8.0pt;font-family:"Times New Roman","serif";
color:windowtext'><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>SEQ Figura \* ARABIC <span style='mso-element:
field-separator'></span></span><![endif]--><span color="windowtext" style="font-family: "Times New Roman","serif"; font-size: 8pt;"><span style="mso-no-proof: yes;">1</span></span><!--[if supportFields]><span style='font-size:8.0pt;
font-family:"Times New Roman","serif";color:windowtext'><span style='mso-element:
field-end'></span></span><![endif]--><span color="windowtext" style="font-family: "Times New Roman","serif"; font-size: 8pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">Deseja-se
reproduzi-la numa folha de papel retangular com 42 cm de comprimento e 30 cm de
altura, deixando livres 3 cm em cada margem, conforme a Figura 2.<o:p></o:p></span></p>
<p align="center" style="background: white; break-after: avoid; margin-bottom: .0001pt; margin: 0cm; page-break-after: avoid; text-align: center;"><span style="color: black; font-size: 10pt; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Imagem_x0020_16"
o:spid="_x0000_i1025" type="#_x0000_t75" style='width:333.75pt;height:280.5pt;
visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><img height="374" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.jpg" v:shapes="Imagem_x0020_16" width="445" /><!--[endif]--></span></p>
<p align="center" class="MsoCaption" style="text-align: center;"><span color="windowtext" style="font-family: "Times New Roman","serif"; font-size: 8pt;">Figura
</span><!--[if supportFields]><span style='font-size:8.0pt;font-family:"Times New Roman","serif";
color:windowtext'><span style='mso-element:field-begin'></span><span
style='mso-spacerun:yes'> </span>SEQ Figura \* ARABIC <span style='mso-element:
field-separator'></span></span><![endif]--><span color="windowtext" style="font-family: "Times New Roman","serif"; font-size: 8pt;"><span style="mso-no-proof: yes;">2</span></span><!--[if supportFields]><span style='font-size:8.0pt;
font-family:"Times New Roman","serif";color:windowtext'><span style='mso-element:
field-end'></span></span><![endif]--><span color="windowtext" style="font-family: "Times New Roman","serif"; font-size: 8pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">A
reprodução da gravura deve ocupar o máximo possível da região disponível,
mantendo-se as proporções da Figura 1<o:p></o:p></span></p>
<p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><span style="border: 1pt none windowtext; color: black; font-size: 8pt; mso-border-alt: none windowtext 0cm; padding: 0cm;">PRADO, A. C. Superinteressante,
ed. 301, fev. 2012 (adaptado).</span><span style="color: black; font-size: 8pt;"><o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">A
escala da gravura reproduzida na folha de papel é:<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%;">A) 1 : 3. </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%;">B) 1 : 4. </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%;">C) 1 : 20. </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b><span style="color: red; font-family: "Calibri","sans-serif"; font-size: 10.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">D) 1 : 25.</span></b><span style="font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%;"> </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: Calibri, "sans-serif"; font-size: 10pt; line-height: 115%;">E) 1 : 32.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><o:p> </o:p></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;">Inicialmente, <span style="mso-spacerun: yes;"> </span>façamos 8m = 800 cm e 6m =600 cm. Como esta
gravura será reduzida em uma folha de papel (igual ao quadro menos as duas bordas)
com dimensões disponíveis. Logo, o comprimento será reduzida a </span></i><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>42 – 3 –<span style='mso-spacerun:yes'> </span>3 = 36 </m:r><m:r>cm</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.0pt; position: relative; top: 4.0pt;"><!--[if gte vml 1]><v:shapetype
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</v:shape><![endif]--><!--[if !vml]--><img height="20" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="120" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;"><span style="mso-spacerun: yes;"> </span>e a largura a <span style="mso-spacerun: yes;"> </span></span></i><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
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color:red'><m:r>30 – 3 – 3 = 24 </m:r><m:r>cm</m:r><m:r>.</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -4.0pt; position: relative; top: 4.0pt;"><!--[if gte vml 1]><v:shape
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<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>R</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>1</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:10.0pt;
mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
mso-bidi-font-family:"Times New Roman";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>800</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r> = 22,22…</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:90.75pt;height:24pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="32" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="121" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Cambria Math","serif"; font-size: 10.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-omath-para: yes;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSub><m:sSubPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>R</m:r></span></i></m:e><m:sub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>2</m:r></span></i></m:sub></m:sSub><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:10.0pt;
mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
mso-bidi-font-family:"Times New Roman";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>600</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>24</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r> </m:r><m:r>= 25</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:69pt;height:24pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="32" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1025" width="92" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Cambria Math","serif"; font-size: 10.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-omath-para: yes;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;">Observe que de acordo com
o comprimento do papel deveríamos reduzir o tamanho da gravura em pouco mais de
22 vezes. Já de acordo com a altura deveríamos reduzir a gravura em 25 vezes. Entretanto,
não podemos usar a redução de 22 vezes porque neste caso a altura não caberia.
Precisamos optar pela redução em que o desenho inteiro cabe na folha (por mais
que sobre um pouco do comprimento).<span style="mso-spacerun: yes;">
</span>Assim, <o:p></o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;line-height:
115%;font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>E</m:r><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>1</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
line-height:115%;font-family:"Cambria Math","serif";mso-bidi-font-family:
"Times New Roman";color:red'><m:r>25</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:30.75pt;height:24pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image009.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="32" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image010.gif" v:shapes="_x0000_i1025" width="41" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;"><o:p> </o:p></span></i></p>
<p class="MsoNormal"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; line-height: 115%;">Portanto, a gravura reproduzida no papel deve ser 25 vezes menor do
que a gravura original, isto é, a escala deverá ser 1: 25.<o:p></o:p></span></i></p><br /><p></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-50602218170385580562022-11-13T12:39:00.004-03:002022-11-13T12:39:58.692-03:00Questão 137 da prova azul do segundo dia do Enem 2016<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem 2016)</span></b><span style="font-size: 10pt; text-align: justify;"> Em uma empresa de móveis, um cliente
encomenda um guarda-roupa nas dimensões 220 cm de altura, 120 cm de largura e
50 cm de profundidade. Alguns dias depois o projetista, com o desenho elaborado
na escala 1:8, entra em contato com o cliente para fazer sua apresentação. No
momento da impressão, o profissional percebe que o desenho não caberia na folha
de papel que costumava usar. Para resolver o problema, configurou a impressora
para que a figura fosse reduzida em 20%.</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">A
altura, a largura e a profundidade do desenho impresso para a apresentação
serão, respectivamente:<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10.0pt;">A) 22,00 cm, 12,00 cm e 5,00 cm.<o:p></o:p></span></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">B)
27,50 cm, 15,00 cm e 6,25 cm.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">C)
34,37 cm, 18,75 cm e 7,81 cm.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">D)
35,20 cm, 19,20 cm e 8,00 cm.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">E)
44,00 cm, 24,00 cm e 10,00 cm.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Primeiro vamos encontrar as dimensões do
guarda-roupa na escala 1:8, em seguida, reduzir 20% do valor encontrado, para
tant,o basta multiplicar o valor encontrado por (1-20%) = 1- 0,2 = 0,8. Assim,
tem-se:<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Altura: </span></i><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>H</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>220</m:r></span></i></m:den></m:f><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:10.0pt;
mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>1</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>8</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r><span style='mso-spacerun:yes'>
</span>⇒</m:r><m:r>H</m:r><m:r>=27,5 </m:r><m:r>cm</m:r><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -19.5pt; position: relative; top: 19.5pt;"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
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<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:106.5pt;
height:30.75pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="142" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>Largura:
</span></i><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>L</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>120</m:r></span></i></m:den></m:f><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:10.0pt;
mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>1</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>8</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r><span style='mso-spacerun:yes'>
</span>⇒</m:r><m:r>L</m:r><m:r>=15 </m:r><m:r>cm</m:r><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -19.5pt; position: relative; top: 19.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:97.5pt;height:30.75pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1025" width="130" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>Profundidade:
</span></i><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>P</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>50</m:r></span></i></m:den></m:f><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span style='font-size:10.0pt;
mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>1</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>8</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r><span style='mso-spacerun:yes'>
</span>⇒</m:r><m:r>P</m:r><m:r>=6,25 </m:r><m:r>cm</m:r><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -19.5pt; position: relative; top: 19.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:102pt;height:30.75pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="41" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="136" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">As dimensões do guarda-roupa após a redução
de 20% feita na impressora são:<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Altura: </span></i><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>27,5×0,8=22 </m:r><m:r>cm</m:r><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:87pt;height:25.5pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image007.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="34" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image008.gif" v:shapes="_x0000_i1025" width="116" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>Largura: </span></i><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>15 ×0,8=12 </m:r><m:r>cm</m:r><m:r><span
style='mso-spacerun:yes'> </span></m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:81.75pt;height:25.5pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image009.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="34" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image010.gif" v:shapes="_x0000_i1025" width="109" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>Profundidade: </span></i><!--[if gte msEquation 12]><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>6,25 ×0,8=5 </m:r><m:r>cm</m:r></span></i></m:oMath><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin; mso-text-raise: -16.5pt; position: relative; top: 16.5pt;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:79.5pt;height:25.5pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image011.png"
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<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Portanto, tem-se 22 cm de altura, 12 cm de
largura e 5 cm de profundidade.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-10804012099389802192022-11-13T12:09:00.004-03:002022-11-13T15:16:46.398-03:00Questão 149 da prova do segundo dia do Enem 2020 Digital<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem 2020 Digital)</span></b><span style="font-size: 10pt; text-align: justify;"> Uma associação desportiva contratou uma
empresa especializada para construir um campo de futebol, em formato
retangular, com 250 metros de perímetro. Foi elaborada uma planta para esse
campo na escala 1 : 2 000.</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">Na
planta, a medida do perímetro do campo de futebol, em metro, é:<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">A)
0,0005<span style="mso-spacerun: yes;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10.0pt;">B)
0,125</span></b><span style="color: black; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span>C) 8 <span style="mso-spacerun: yes;"> </span>D) 250 <span style="mso-spacerun: yes;"> </span>E) 500 000.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Basta utilizar uma regra de três simples.<span style="mso-spacerun: yes;"> </span>Como a escala é 1:2000, então:<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">1 m no
papel →<span style="mso-spacerun: yes;"> </span>2000 m na realidade<o:p></o:p></span></i></p>
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">x m no
papel →<span style="mso-spacerun: yes;"> </span>250 m na realidade<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>x</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>250</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>1</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2000</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";color:red'><m:r>
⇒</m:r><m:r>x</m:r><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>250</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>2000</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>25</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>200</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>1</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>8</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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</v:shape><![endif]--><!--[if !vml]--><img height="33" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" v:shapes="_x0000_i1025" width="259" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-69658253220318236552022-11-13T12:00:00.001-03:002022-11-13T12:00:06.566-03:00Questão 169 da prova azul do segundo dia do Enem 2018<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem 2018)</span></b><span style="font-size: 10pt; text-align: justify;"> Uma empresa de comunicação tem a tarefa
de elaborar um material publicitário de um estaleiro para divulgar um novo
navio, equipado com um guindaste de 15 m de altura e uma esteira de 90 m de
comprimento. No desenho desse navio, a representação do guindaste deve ter sua
altura entre 0,5 cm e 1 cm, enquanto a esteira deve apresentar comprimento
superior a 4 cm. Todo o desenho deverá ser feito em uma escala 1 : X.</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">Os
valores possíveis para X são, apenas,<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">A)
X > 1 500.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>B) X < 3 000.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10.0pt;">C)
1 500 < X < 2 250.</span></b><span style="color: black; font-size: 10.0pt;"><span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span>D) 1
500 < X < 3 000. <span style="mso-spacerun: yes;"> </span></span><span style="font-size: 10.0pt;">E)<span style="color: black;"> 2 500 < X < 3 000.</span><o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Sabendo que a escala é dada pela a razão entre a medida do desenho e
a medida da realidade, tem-se:<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">A unidade no desenho é cm. Então:<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">15 m = 1500 cm e 90 m = 9000 cm<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoListParagraph" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 54.0pt; margin-right: 0cm; margin-top: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -36.0pt; text-justify: inter-ideograph;"><!--[if !supportLists]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">i)<span style="font: 7.0pt "Times New Roman";">
</span></span></span></i><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">No
desenho, a altura do guindaste deve estar entre 0,5 cm e 1 cm. Tem-se:<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
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mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>1</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
normal'><span style='font-size:10.0pt;font-family:"Cambria Math","serif";
mso-bidi-font-family:"Times New Roman";color:red'><m:r>x</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
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mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>0,5 </m:r><m:r>cm</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>1500 </m:r><m:r>cm</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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style='mso-spacerun:yes'> </span>⇒</m:r><m:r>x</m:r><m:r>=3000</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shapetype
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<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
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mso-bidi-font-family:"Times New Roman";color:red'><m:r>x</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>1 </m:r><m:r>cm</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>1500 </m:r><m:r>cm</m:r></span></i></m:den></m:f><i
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style='mso-spacerun:yes'> </span>⇒</m:r><m:r>x</m:r><m:r>=1500</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><!--[if !vml]--><img height="32" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" v:shapes="_x0000_i1025" width="154" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Para o guindaste, devemos ter </span></i><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">1 500 < x < 3 000.<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoListParagraph" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 54.0pt; margin-right: 0cm; margin-top: 0cm; mso-add-space: auto; mso-list: l0 level1 lfo1; text-align: justify; text-indent: -36.0pt; text-justify: inter-ideograph;"><!--[if !supportLists]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">ii)<span style="font: 7.0pt "Times New Roman";">
</span></span></span></i><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">No
desenho, o comprimento da esteira deve ser maior que 4 cm. Tem-se<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:f><m:fPr><span
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mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
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style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>1</m:r></span></i></m:num><m:den><i style='mso-bidi-font-style:
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mso-bidi-font-family:"Times New Roman";color:red'><m:r>X</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";mso-bidi-font-family:"Times New Roman";
color:red;font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>4 </m:r><m:r>cm</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";mso-bidi-font-family:"Times New Roman";
color:red'><m:r>9000 </m:r><m:r>cm</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
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style='mso-spacerun:yes'> </span>⇒</m:r><m:r>x</m:r><m:r>=2250 </m:r><m:r>cm</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><!--[if !vml]--><img height="32" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" v:shapes="_x0000_i1025" width="176" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Se o comprimento no desenho deve ser maior que 4, então x deve ser
menor que 2250, ou seja,<span style="mso-spacerun: yes;"> </span>x < 2250.<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Por (i) e (ii) tem-se que </span></i><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">1 500 < X < 2 250.</span></i><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-64081384651599530852022-11-13T11:42:00.004-03:002022-11-13T11:43:05.104-03:00Questão 174 da prova azul do segundo dia do Enem 2013<p> <b style="text-align: justify;"><span style="font-size: 10pt;">(Enem 2013)</span></b><span style="font-size: 10pt; text-align: justify;"> A figura apresenta dois mapas, em que o
estado do Rio de Janeiro é visto em diferentes escalas.</span></p>
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style='width:295.5pt;height:207.75pt;visibility:visible;mso-wrap-style:square'>
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<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">Há
interesse em estimar o número de vezes que foi ampliada a área correspondente a
esse estado no mapa do Brasil.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">Esse
número é:<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">A)
menor que 10.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">B)
maior que 10 e menor que 20.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">C)
maior que 20 e menor que 30.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 10.0pt;">D) maior que 30 e menor que 40.<o:p></o:p></span></b></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;">E)
maior que 40.<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10.0pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;">Processo Resolutivo<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">A escala apresenta a relação entre duas medidas,
a do desenho e a real. No mapa do Brasil, 1 unidade do desenho equivale a 25.000.000
do real. Já no mapa do Rio de Janeiro, 1 unidade equivale<span style="mso-spacerun: yes;"> </span>a 4.000.000 do real.<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Assim, temos:<o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>k</m:r><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>25000000</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>4000000</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>25</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>4</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
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</v:shape><![endif]--><!--[if !vml]--><img height="49" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image003.gif" v:shapes="_x0000_i1025" width="116" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Logo, <o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><!--[if gte msEquation 12]><m:oMathPara><m:oMath><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>k</m:r></span></i></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:
10.0pt;font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>25</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>4</m:r></span></i></m:den></m:f></m:e></m:d></m:e><m:sup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>2</m:r></span></i></m:sup></m:sSup><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>=</m:r></span></i><m:f><m:fPr><span
style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt;
font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";color:red;font-style:italic;
mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>625</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;
font-family:"Cambria Math","serif";color:red'><m:r>16</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-size:10.0pt;font-family:
"Cambria Math","serif";color:red'><m:r>=39,0625</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;"><!--[if gte vml 1]><v:shape
id="_x0000_i1025" type="#_x0000_t75" style='width:126.75pt;height:39pt'>
<v:imagedata src="file:///C:\Users\MATEUS~1\AppData\Local\Temp\msohtmlclip1\01\clip_image004.png"
o:title="" chromakey="white"/>
</v:shape><![endif]--><!--[if !vml]--><img height="52" src="file:///C:/Users/MATEUS~1/AppData/Local/Temp/msohtmlclip1/01/clip_image005.gif" v:shapes="_x0000_i1025" width="169" /><!--[endif]--></span><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p></o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;"><o:p> </o:p></span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10.0pt;">Então, o número de vezes que foi ampliada a
área é um um número maior que 30 e menor que 40.<o:p></o:p></span></i></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-34852231089490453122022-11-13T11:32:00.002-03:002022-11-13T11:33:22.889-03:00Questão 136 da prova azul do segundo dia do Enem 2012<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b><span style="font-size: 10pt;">(Enem 2012)</span></b><span style="font-size: 10pt;"> O esporte de alta competição da
atualidade produziu uma questão ainda sem resposta: Qual é o limite do corpo
humano? O maratonista original, o grego da lenda, morreu de fadiga por ter
corrido 42 quilômetros. O americano Dean Karnazes, cruzando sozinho as
planícies da Califórnia, conseguiu correr dez vezes mais em 75 horas.<o:p></o:p></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;">Um
professor de Educação Física, ao discutir com a turma o texto sobre a
capacidade do maratonista americano, desenhou na lousa uma pista reta de 60
centímetros, que representaria o percurso referido.<o:p></o:p></span></p><p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><span style="border: 1pt none windowtext; font-size: 8pt; padding: 0cm;">Disponível em:
http://veja.abril.com.br. Acesso em: 25 jun. 2011 (adaptado).</span><span style="font-size: 8pt;"><o:p></o:p></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;">Se
o percurso de Dean Karnazes fosse também em uma pista reta, qual seria a escala
entre a pista feita pelo professor e a percorrida pelo atleta?<o:p></o:p></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;"> </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;">A)
1:700 </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;">B) 1:7 000 </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;">C) 1:70 000 </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;">D) 1:700 000 </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;">E) 1:7 000 000<o:p></o:p></span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;"> </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;"> </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i><span style="color: red; font-size: 10pt;">A escala mostra a razão entre o desenho e a
realidade. Assim, o atleta percorreu uma distância dez vezes maior que a
maratona, portanto 420Km, convertendo esta distância para centímetros, 420Km=
42000000cm, assim <o:p></o:p></span></i></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i><span style="color: red; font-size: 10pt;"> </span></i></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><br /></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"></p><div class="separator" style="clear: both; text-align: center;"><img alt="" border="0" class="placeholder" height="240" id="f42d8d697e8a1" src="https://www.blogger.com/img/transparent.gif" style="background-color: #d8d8d8; background-image: url('https://fonts.gstatic.com/s/i/materialiconsextended/insert_photo/v6/grey600-24dp/1x/baseline_insert_photo_grey600_24dp.png'); background-position: 50% 50%; background-repeat: no-repeat; opacity: 0.6;" width="320" /></div><br /><br /><p></p><p>
</p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-size: 10pt;"> </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><br /></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-8712267463212906682022-11-13T11:21:00.003-03:002022-11-13T11:32:45.349-03:00Questão 145 da prova azul do segundo dia do Enem 2012<p><b style="text-align: justify;"><span style="font-size: 10pt;">(Enem 2012)</span></b><span style="font-size: 10pt; text-align: justify;"> Um biólogo mediu a altura de cinco
árvores distintas e representou-as em uma mesma malha quadriculada, utilizando
escalas diferentes, conforme indicações na figura a seguir.</span></p>
<p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"><br /></p><p align="center" style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><img alt="" border="0" class="placeholder" height="240" id="251fd72d879ab" src="https://www.blogger.com/img/transparent.gif" style="background-color: #d8d8d8; background-image: url('https://fonts.gstatic.com/s/i/materialiconsextended/insert_photo/v6/grey600-24dp/1x/baseline_insert_photo_grey600_24dp.png'); background-position: 50% 50%; background-repeat: no-repeat; opacity: 0.6;" width="320" /></div><br /><br /></div><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;">Qual
é a árvore que apresenta a maior altura real?<o:p></o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;"><o:p> </o:p></span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span face="Calibri, "sans-serif"" style="font-size: 10pt; line-height: 115%;">A) I </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span face="Calibri, "sans-serif"" style="font-size: 10pt; line-height: 115%;">B)
II </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span face="Calibri, "sans-serif"" style="font-size: 10pt; line-height: 115%;">C) III </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><b><span face=""Calibri","sans-serif"" style="color: red; font-size: 10pt; line-height: 115%; mso-ansi-language: PT-BR; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: PT-BR; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: minor-latin;">D) IV</span></b><span face="Calibri, "sans-serif"" style="font-size: 10pt; line-height: 115%;"> </span></p><p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span face="Calibri, "sans-serif"" style="font-size: 10pt; line-height: 115%;">E) V</span></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: black; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></p>
<p style="background: white; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">Sendo
ℓ a medida do lado de cada quadrado, tem-se em<o:p></o:p></span></i></p>
<p style="background: white; text-align: justify; text-justify: inter-ideograph;"></p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><img alt="" border="0" class="placeholder" height="240" id="68eb77fb9552f" src="https://www.blogger.com/img/transparent.gif" style="background-color: #d8d8d8; background-image: url('https://fonts.gstatic.com/s/i/materialiconsextended/insert_photo/v6/grey600-24dp/1x/baseline_insert_photo_grey600_24dp.png'); background-position: 50% 50%; background-repeat: no-repeat; opacity: 0.6;" width="320" /></div><br /><br /></div><p></p><p style="background: white; text-align: justify; text-justify: inter-ideograph;"><i><span style="color: red; font-size: 10pt;">Assim,
as alturas das árvores I, II, III, IV e
V, são respectivamente: 900ℓ, 450ℓ, 900ℓ, 1350ℓ e 675ℓ.</span></i></p>
<p style="background: white; margin-bottom: .0001pt; margin: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-size: 10pt;">Portanto, a árvore IV tem a maior altura
real</span></i><span style="color: black; font-size: 10pt;">.<o:p></o:p></span></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-52801305112225762932022-11-13T11:06:00.004-03:002022-11-13T11:34:29.969-03:00Questão 161 da prova azul do segundo dia do Enem 2011<p><b style="text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">(Enem
2011)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt; text-align: justify;">
Cerca de 20 milhões de brasileiros vivem na região coberta pela Caatinga, em
quase 800 mil km² de área. Quando não chove, o homem do sertão e sua família
precisam caminhar quilômetros em busca da água dos açudes. A irregularidade
climática é um dos fatores que mais interferem na vida do sertanejo.</span></p>
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="font-family: "Times New Roman","serif"; font-size: 8pt;">Disponível em: http://www.wwf.org.br. Acesso em: 23
abr. 2010.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 10pt;">Segundo esse
levantamento, a densidade demográfica da região coberta pela caatinga, em
habitantes por km², é de:</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">A) 250.<span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><b style="mso-bidi-font-weight: normal;"><span style="color: red;">B) 25.</span></b><span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">C) 2,5.<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">D) 0,25.<span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">E) 0,025.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">A densidade demográfica da região coberta pela caatinga, em
habitantes por km², é de:<o:p></o:p></span></i></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><br /></span></i></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"></span></i></p><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj8lDaYOz36aVJQxMdq5Nx6j4q9PNMILPSGkrQ95qj9iA5nqxLrHY2od-2GlcxFHXPiz3suCVE_NUMi2IU4cGcKlGJFexUN-suHFSpZrFNAmfgwDAZjCE5OYAywIFwaVfOg8Jfm-J8iRun7feAEgHKfFbtMXgSS3wu7C009quvRUcx8aX1QWzNSAP39jA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="49" data-original-width="272" height="58" src="https://blogger.googleusercontent.com/img/a/AVvXsEj8lDaYOz36aVJQxMdq5Nx6j4q9PNMILPSGkrQ95qj9iA5nqxLrHY2od-2GlcxFHXPiz3suCVE_NUMi2IU4cGcKlGJFexUN-suHFSpZrFNAmfgwDAZjCE5OYAywIFwaVfOg8Jfm-J8iRun7feAEgHKfFbtMXgSS3wu7C009quvRUcx8aX1QWzNSAP39jA" width="320" /></a></div><br /><br /></div><i style="mso-bidi-font-style: normal;"><br /><br /></i></div><i style="mso-bidi-font-style: normal;"><br /><br /></i></div><div class="separator" style="clear: both; text-align: center;"><i style="mso-bidi-font-style: normal;"><br /></i></div><i style="mso-bidi-font-style: normal;"><br /><br /></i><p></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-42040883632920665242022-11-13T11:00:00.007-03:002022-11-13T11:34:52.951-03:00Questão 146 da prova azul do segundo dia do Enem 2011<p><b style="text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">(Enem
2011)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt; text-align: justify;">
Sabe-se que a distância real, em linha reta, de uma cidade A, localizada no
estado de São Paulo, a uma cidade B, localizada no estado de Alagoas, é igual a
2 000 km. Um estudante, ao analisar um mapa, verificou com sua régua que a
distância entre essas duas cidades, A e B, era 8 cm.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">Os dados nos
indicam que o mapa observado pelo estudante está na escala de:<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">A) 1 : 250.<span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">B) 1 : 2 500.<span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">C )1 : 25 000.<span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">D) 1 : 250 000.<span style="mso-spacerun: yes;"> </span><b style="mso-bidi-font-weight: normal;"><span style="color: red;"><span style="mso-spacerun: yes;"> </span></span></b></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><b style="mso-bidi-font-weight: normal;"><span style="color: red;">E) 1 : 25 000 000.</span></b><o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><i>O mapa
observado pelo estudante está na escala de:</i><o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p></o:p></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhg1rKqs62KnZpDHgvIXuOaPA0mVxe4HN6q6ItPz5ME9KBiB67zr6V2NBd-ViXiFaEjj_RYs3Xzx_oDISX83Wi7H_TWfun0wa4dwVBLn3wwkYZKJPs4lGX1bdrhcPkuDCZgFUvAa5gFoGRR64Xcfstv0klsp169lpVrvAgeYaiokWWzyTu-6K7tQxM-XA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="46" data-original-width="360" height="41" src="https://blogger.googleusercontent.com/img/a/AVvXsEhg1rKqs62KnZpDHgvIXuOaPA0mVxe4HN6q6ItPz5ME9KBiB67zr6V2NBd-ViXiFaEjj_RYs3Xzx_oDISX83Wi7H_TWfun0wa4dwVBLn3wwkYZKJPs4lGX1bdrhcPkuDCZgFUvAa5gFoGRR64Xcfstv0klsp169lpVrvAgeYaiokWWzyTu-6K7tQxM-XA" width="320" /></a></div><br /><br /><p></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-19846698435178958072022-11-13T10:55:00.005-03:002022-11-13T11:35:07.909-03:00Questão 137 da prova azul do segundo dia do Enem 2011<p> <b style="text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">(Enem
2010)</span></b><span style="font-family: "Times New Roman", "serif"; font-size: 10pt; text-align: justify;">
No monte de Cerro Armazones, no deserto de Atacama, no Chile, ficará o maior
telescópio da superfície terrestre, o Telescópio Europeu Extremamente Grande
(E-ELT) O E-ELT terá um espelho primário de 42 m de diâmetros, “maior olho do
mundo voltado para o céu”.</span></p>
<p align="center" class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: center;"><span style="font-family: "Times New Roman","serif"; font-size: 8pt;">Disponível em: http://www.estadao.com.br. Acesso em:
27 abr. 2010 (adaptado).<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">Ao ler esse
texto em uma sala de aula, uma professora fez uma suposição de que o diâmetro
do olho humano mede aproximadamente 2,1 cm.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">Qual a razão
entre o diâmetro aproximado do olho humano, suposto pela professora, e o
diâmetro do espelho primário do telescópio citado?<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">A) 1 : 20<span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">B) 1 : 100<span style="mso-spacerun: yes;"> </span><b style="mso-bidi-font-weight: normal;"><span style="color: red;"><span style="mso-spacerun: yes;"> </span></span></b></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><b style="mso-bidi-font-weight: normal;"><span style="color: red;">C) 1 :
200<span style="mso-spacerun: yes;"> </span></span></b></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;">D) 1 : 1 000<span style="mso-spacerun: yes;"> </span></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><span style="mso-spacerun: yes;"></span>E) 1 : 2 000<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><span style="font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Processo Resolutivo<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;"><o:p> </o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"><i style="mso-bidi-font-style: normal;"><span style="color: red; font-family: "Times New Roman","serif"; font-size: 10pt;">Sendo de 42 m = 4200 cm o diâmetro do espelho primário do telescópio
e 2,1 cm o diâmetro do olho humano, a razão entre o diâmetro aproximado do olho
humano e o diâmetro primário do telescópio citado é:<o:p></o:p></span></i></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-align: justify; text-justify: inter-ideograph;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiIyM70f_doIXvj0I8donXz4dCOIoDMzTRd9dtZVL4H63w0oXEXBXmpXMquJZFxnlBo_a6EZ-iDKd5R0ua74swbC6ST_GvU8J7JFnh1SykuQb0faJhbTGQ-L_kCpF1jzrDLjwsk7ClH1w1ikLVCF7tspjgyYRmhdX_IM_oSlPbJJ3Js3sci2ueOrb4McQ" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="46" data-original-width="233" height="63" src="https://blogger.googleusercontent.com/img/a/AVvXsEiIyM70f_doIXvj0I8donXz4dCOIoDMzTRd9dtZVL4H63w0oXEXBXmpXMquJZFxnlBo_a6EZ-iDKd5R0ua74swbC6ST_GvU8J7JFnh1SykuQb0faJhbTGQ-L_kCpF1jzrDLjwsk7ClH1w1ikLVCF7tspjgyYRmhdX_IM_oSlPbJJ3Js3sci2ueOrb4McQ" width="320" /></a></div><br /><br /><p></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-90794662375986676802022-11-03T09:35:00.003-03:002022-11-03T09:35:48.744-03:00O Problema do Sofá em Movimento<p style="text-align: justify;"><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px;"><b>O matemático Leo Moser colocou em 1966 o seguinte curioso problema matemático: "qual é a forma da maior área do avião que pode ser movida em torno de um canto em ângulo reto em um corredor bidimensional de largura 1?"</b></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;">Podemos começar com um quadrado 1 por 1.</span></p><div class="q-box" style="background-color: white; box-sizing: border-box; color: #282829; filter: blur(0px); font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin-bottom: 1em; position: relative; transition-duration: 1s; transition-property: undefined; transition-timing-function: ease-out;"><img class="q-image qu-cursor--default qu-display--block qu-borderRadius--small" src="https://qph.cf2.quoracdn.net/main-qimg-859c78b91489f0e81720c973849503b1" style="border-radius: 3px; border-style: none; box-sizing: border-box; cursor: default; display: block; margin-left: auto; margin-right: auto; max-width: 100%;" /></div><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;">Esse semicírculo com raio 1 se sai melhor. Tem área π2.</span></p><div class="q-box" style="background-color: white; box-sizing: border-box; color: #282829; filter: blur(0px); font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin-bottom: 1em; position: relative; transition-duration: 1s; transition-property: undefined; transition-timing-function: ease-out;"><img class="q-image qu-cursor--default qu-display--block qu-borderRadius--small" src="https://qph.cf2.quoracdn.net/main-qimg-76ad42ef0094d02edf821a7478f1b4d4" style="border-radius: 3px; border-style: none; box-sizing: border-box; cursor: default; display: block; margin-left: auto; margin-right: auto; max-width: 100%;" /></div><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;">Podemos continuar a fazer melhorias. O matemático John Hammersley notou que, se o semicírculo for cortado em dois quartos de círculo, que são separados e o espaço entre eles preenchido com um bloco retangular, obtemos uma forma de sofá maior, que pode ser movida na esquina se apenas um buraco semicircular menor também for removido do bloco retangular.</span></p><div class="q-box" style="background-color: white; box-sizing: border-box; color: #282829; filter: blur(0px); font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin-bottom: 1em; position: relative; transition-duration: 1s; transition-property: undefined; transition-timing-function: ease-out;"><img class="q-image qu-cursor--default qu-display--block qu-borderRadius--small" src="https://qph.cf2.quoracdn.net/main-qimg-b0cf7a9331eb01efa14dcbe4c25f9797" style="border-radius: 3px; border-style: none; box-sizing: border-box; cursor: default; display: block; margin-left: auto; margin-right: auto; max-width: 100%;" /></div><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;">Em 1992, Joseph Gerver encontrou uma forma melhor, com uma área um pouco maior de cerca de 2.2195. Gerver não conseguiu provar que sua solução era ótima. Até hoje, 50 anos após a pergunta, ainda é a melhor solução.</span></p><div class="q-box" style="background-color: white; box-sizing: border-box; color: #282829; filter: blur(0px); font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin-bottom: 1em; position: relative; transition-duration: 1s; transition-property: undefined; transition-timing-function: ease-out;"><img class="q-image qu-cursor--default qu-display--block qu-borderRadius--small" src="https://qph.cf2.quoracdn.net/main-qimg-ebc2ae295bd2d17c77d0a80c1cd71cc7" style="border-radius: 3px; border-style: none; box-sizing: border-box; cursor: default; display: block; margin-left: auto; margin-right: auto; max-width: 100%;" /></div><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;">Tentativas de encontrar limites superiores foram feitas. Os matemáticos definiram uma "constante do sofá", que é apenas a resposta para esse problema! Yoav Kallus e Dan Romik provaram um limite superior em junho de 2017, limitando o sofá constantemente a 2,37.</span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><br /></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><b>Referências:</b></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><span style="font-size: x-small;">D. Romik. Equações diferenciais e soluções exatas no problema do sofá em movimento. Para aparecer em Matemática Experimental.</span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><span style="font-size: x-small;">Y. Kallus, D. Romik. Limites superiores aprimorados no problema do sofá em movimento. Pré-impressão, 2017.</span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><span style="font-size: x-small;">Movendo o problema do sofá na Wikipedia.</span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><span style="font-size: x-small;">E. W. Weisstein. Movendo o problema do sofá no Wolfram MathWorld.</span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><span style="font-size: x-small;">J. L. Gerver. Ao mover um sofá em uma esquina. Geometriae Dedicata 42 (1992), 267-283. doi: 10.1007 / BF02414066.</span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;"><span style="font-size: x-small;">P. Gibbs. Um estudo computacional de sofás e carros. Pré-impressão, 2014.</span></span></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-51414786187015974342022-11-03T09:26:00.003-03:002022-11-03T09:28:00.563-03:00Quadrados Iguais<p><span face="-apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif" style="color: #282829; font-size: 15px;"><b>Dois quadrados de lado 1 têm um centro comum. Mostre que a área da interseção é maior que 3/4.</b></span></p><div class="q-box" style="background-color: white; box-sizing: border-box; color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin-left: -16px; margin-right: -16px;"><div class="q-box" style="box-sizing: border-box; filter: blur(0px); margin-bottom: 1em; position: relative; transition-duration: 1s; transition-property: undefined; transition-timing-function: ease-out;"><img class="q-image qu-cursor--default qu-display--block" src="https://qph.cf2.quoracdn.net/main-qimg-dc4e9fb55d74700cb069facbc5179eb3" style="border-style: none; box-sizing: border-box; cursor: default; display: block; margin-left: auto; margin-right: auto; max-width: 100%;" /></div></div><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; text-align: center; word-break: break-word;"><span style="background: none; font-weight: bold;">Solução</span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span style="background: none;">Observe que um dos quadrados pode ser obtido do outro via rotação ao redor do centro comum. Essa rotação delineia um círculo inscrito no quadrado. Assim, a área da interseção deve ser maior que á área do círculo, a qual é π/4 e que é maior que 3/4.</span></p><div class="q-box" style="background-color: white; box-sizing: border-box; color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin-left: -16px; margin-right: -16px;"><div class="q-box" style="box-sizing: border-box; filter: blur(0px); margin-bottom: 1em; position: relative; transition-duration: 1s; transition-property: undefined; transition-timing-function: ease-out;"><img class="q-image qu-cursor--default qu-display--block" src="https://qph.cf2.quoracdn.net/main-qimg-e17ff60c0d60578595d2a0c95e6b588f" style="border-style: none; box-sizing: border-box; cursor: default; display: block; margin-left: auto; margin-right: auto; max-width: 100%;" /></div></div>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0tag:blogger.com,1999:blog-2757809063160420199.post-34923622329799945552022-10-09T13:22:00.001-03:002022-10-09T13:23:10.176-03:00Número Euleriano ou Constante de Napier<p style="text-align: justify;"> <span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">Você sabia que "<b><i>e</i></b>" </span><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">(</span><span style="background-color: white; color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px;">2,71828...)</span><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;"> </span><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">é uma constante numérica, a</span><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px;">ssim como, pi (3,14159...). </span></p><p style="text-align: justify;"><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">O valor de "<b><i>e</i></b>" </span><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">é encontrado em muitas fórmulas matemáticas, como aquelas que descrevem um aumento ou diminuição não linear, como crescimento ou decaimento (incluindo juros compostos), a "curva de sino" estatística, a forma de um cabo suspenso ou um arco permanente. </span></p><p style="text-align: justify;"><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">Esse número irracional e transcendente também aparece em alguns problemas de probabilidade, alguns problemas de contagem e até mesmo no estudo da distribuição de números primos. </span><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">No campo da avaliação não destrutiva ela é encontrada em fórmulas como as usadas para descrever a atenuação do ultrassom em um material. </span><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">A energia sonora decai à medida que se afasta da fonte sonora por um fator relativo a "<b><i>e</i></b>". </span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; text-align: justify; word-break: break-word;"><span style="background: none;">Seu valor mais utilizado é de aproximadamente 2,71828, entretanto já foram calculado, </span>por Sebastian Wedeniwski, <span style="background-color: initial;">869.894.101 casas decimais deste número. </span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; direction: ltr; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; text-align: center; word-break: break-word;"><span style="background-color: initial; font-size: 15px;"><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, Segoe UI, Roboto, Oxygen-Sans, Ubuntu, Cantarell, Helvetica Neue, sans-serif;"><i><b>e = 2,71828182845904523536028747135266...</b></i></span></span></p><p><span style="color: #282829; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; vertical-align: inherit;">O valor de "<b><i>e</i></b>" pode ser encontrado quando se aplica o limite n tendo ao mais infinito na na expressão </span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span class="QTextMath__QTextMathWrapper-sc-13yf4r2-0 kMHVwX qtext_span qtext_math" style="direction: ltr; display: inline-block; margin: -2px -1px !important; max-height: 600px; max-width: 100%; overflow-wrap: break-word; overflow: auto hidden; padding: 2px !important; unicode-bidi: isolate; vertical-align: bottom;"></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><span class="QTextMath__QTextMathWrapper-sc-13yf4r2-0 kMHVwX qtext_span qtext_math" style="direction: ltr; display: inline-block; margin: -2px -1px !important; max-height: 600px; max-width: 100%; overflow-wrap: break-word; overflow: auto hidden; padding: 2px !important; unicode-bidi: isolate; vertical-align: bottom;"><span class="MathJax" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mi>n</mi></mfrac><mo>)</mo></mrow><mi>n</mi></msup></math>" id="MathJax-Element-109-Frame" role="presentation" style="border: 0px; direction: ltr; display: inline-table; float: none; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 0px; position: relative; white-space: nowrap; word-spacing: normal;" tabindex="0"><nobr aria-hidden="true" style="border: 0px; line-height: normal; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; padding: 0px; transition: none 0s ease 0s; vertical-align: 0px;"><span class="math" id="MathJax-Span-968" style="border: 0px; box-sizing: content-box; display: inline-block; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 4.601em;"><span style="border: 0px; box-sizing: content-box; display: inline-block; font-size: 17.4px; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.968em;"><span style="border: 0px; box-sizing: content-box; clip: rect(1.21em, 1003.97em, 2.819em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.296em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-969" style="border: 0px; box-sizing: content-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-970" style="border: 0px; box-sizing: content-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 3.968em;"><span style="border: 0px; box-sizing: content-box; clip: rect(2.991em, 1003.28em, 4.543em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.02em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-971" style="border: 0px; box-sizing: content-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mo" id="MathJax-Span-972" style="border: 0px; box-sizing: content-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em;"><span style="border: 0px; box-sizing: content-box; font-family: MathJax_Size1; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="transition: none 0s ease 0s; vertical-align: inherit;"><span style="transition: none 0s ease 0s; vertical-align: inherit;">(</span></span></span></span><span class="mn" id="MathJax-Span-973" style="border: 0px; box-sizing: content-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="transition: none 0s ease 0s; vertical-align: inherit;"><span style="transition: none 0s ease 0s; vertical-align: inherit;"> 1 </span></span></span><span class="mo" id="MathJax-Span-974" style="border: 0px; box-sizing: content-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.233em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="transition: none 0s ease 0s; vertical-align: inherit;"><span style="transition: none 0s ease 0s; vertical-align: inherit;">+</span></span></span><span class="mfrac" id="MathJax-Span-975" style="border: 0px; box-sizing: content-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.233em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.118em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.52em;"><span style="border: 0px; box-sizing: content-box; clip: rect(3.394em, 1000.29em, 4.198em, -999.997em); left: 4.51562px; line-height: normal; margin: 0px 0px 0px -0.17em; padding: 0px; position: absolute; top: -4.422em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-976" style="border: 0px; box-sizing: content-box; display: inline; font-family: MathJax_Main; font-size: 12.3018px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="transition: none 0s ease 0s; vertical-align: inherit;"><span style="transition: none 0s ease 0s; vertical-align: inherit;">1</span></span></span><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 4.026em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: content-box; clip: rect(3.566em, 1000.4em, 4.198em, -999.997em); left: 4.51562px; line-height: normal; margin: 0px 0px 0px -0.227em; padding: 0px; position: absolute; top: -3.675em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-977" style="border: 0px; box-sizing: content-box; display: inline; font-family: MathJax_Math-italic; font-size: 12.3018px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="transition: none 0s ease 0s; vertical-align: inherit;"><span style="transition: none 0s ease 0s; vertical-align: inherit;">n</span></span></span><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 4.026em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: content-box; clip: rect(0.865em, 1000.52em, 1.267em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.319em; transition: none 0s ease 0s; vertical-align: 0px;"><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: initial; border-right-style: initial; border-top-style: solid; border-width: 1.3px 0px 0px; box-sizing: content-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em; width: 0.52em;"></span><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 1.095em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="mo" id="MathJax-Span-978" style="border: 0px; box-sizing: content-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0em;"><span style="border: 0px; box-sizing: content-box; font-family: MathJax_Size1; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span style="transition: none 0s ease 0s; vertical-align: inherit;"><span style="transition: none 0s ease 0s; vertical-align: inherit;">)</span></span></span></span></span><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 4.026em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; box-sizing: content-box; left: 3.451em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.652em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" id="MathJax-Span-979" style="border: 0px; box-sizing: content-box; display: inline; font-family: MathJax_Math-italic; font-size: 12.3018px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">n</span><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 4.026em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; box-sizing: content-box; display: inline-block; height: 2.302em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-bottom-style: initial; border-color: initial; border-image: initial; border-left-style: solid; border-right-style: initial; border-top-style: initial; border-width: 0px; box-sizing: content-box; display: inline-block; height: 1.603em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: -0.463em; width: 0px;"></span></span></nobr><br /></span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; word-break: break-word;"><br /></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; text-align: justify; word-break: break-word;"><span style="background: none;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">O número "<b><i>e</i></b>" foi estudado pela primeira vez pelo matemático suíço Leonhard Euler na década de 1720, embora sua existência estivesse mais ou menos implícita no trabalho de John Napier, o inventor dos logaritmos, em 1614. </span></span></span><span style="background-color: initial; vertical-align: inherit;">Euler também foi o primeiro a usar a letra e para em 1727 (o fato de ser a primeira letra de seu sobrenome é coincidência). </span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; text-align: justify; word-break: break-word;"><span style="background-color: initial; vertical-align: inherit;">Como resultado, às vezes e é chamado de Número Euleriano ou Constante de Napier. </span><span style="background-color: initial; vertical-align: inherit;">Foi provado por Euler que "<b><i>e</i></b>" é um número irracional, então sua expansão decimal nunca termina, nem é periódica.</span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px 0px 1em; overflow-wrap: anywhere; padding: 0px; text-align: justify; word-break: break-word;"><span style="background: none;"><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">Outra maneira eficaz de calcular o valor de "<b><i>e</i></b>" é por meio da </span></span><span style="vertical-align: inherit;"><span style="vertical-align: inherit;">soma infinita de fatoriais como denominadores do numerador 1. </span><span style="vertical-align: inherit;">Assim, </span></span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px; overflow-wrap: anywhere; padding: 0px; text-align: center; word-break: break-word;"><span style="background: none;"><span style="vertical-align: inherit;"><i><span style="vertical-align: inherit;">e = 1/0! </span><span style="vertical-align: inherit;">+ 1/1! </span><span style="vertical-align: inherit;">+ 1/2! </span><span style="vertical-align: inherit;">+ 1/3! </span><span style="vertical-align: inherit;">+ 1/4! </span><span style="vertical-align: inherit;">+ ...</span></i></span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px; overflow-wrap: anywhere; padding: 0px; text-align: center; word-break: break-word;"><span style="background: none;"><span style="vertical-align: inherit;"><b><span style="vertical-align: inherit;"><br /></span></b></span></span></p><p class="q-text qu-display--block qu-wordBreak--break-word qu-textAlign--start" style="background-color: white; box-sizing: border-box; color: #282829; direction: ltr; font-family: -apple-system, system-ui, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-size: 15px; margin: 0px; overflow-wrap: anywhere; padding: 0px; text-align: justify; word-break: break-word;"><span style="background: none;"><span style="vertical-align: inherit;"><b><span style="vertical-align: inherit;">Existem outras maneiras de encontrar essa constante, você sabe dizer quais?</span></b></span></span></p>MatheusMathicahttp://www.blogger.com/profile/14116618159109622876noreply@blogger.com0