tag:blogger.com,1999:blog-19405760586078232742024-03-05T05:22:46.929-08:00AS FACES DA MATEMÁTICASeu portal de conteúdo atualizado
Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.comBlogger374125tag:blogger.com,1999:blog-1940576058607823274.post-72718213186576483702024-02-04T18:36:00.000-08:002024-02-08T14:38:20.085-08:00(OBJETIVA CONCURSOS) - QUESTÃO<div style="text-align: justify;">Assinalar a alternativa que apresenta as coordenadas dos focos da elipse que possui equação</div><div style="text-align: justify;"><br /></div><div style="text-align: center;"><span class="mstyle" face=""Source Sans Pro", "Trebuchet MS", Tahoma, sans-serif" id="MathJax-Span-36" style="background-color: white; border: 0px; box-sizing: border-box; color: #333333; display: inline; font-size: 16.128px; line-height: normal; margin: 0px; padding: 0px; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-37" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-38" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.127em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.615em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.041em, 1001em, 4.219em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.493em; padding: 0px; position: absolute; top: -4.709em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-39" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.995em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.413em, 1000.5em, 4.219em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-40" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.561em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.399em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-41" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; font-size: 11.4025px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(3.165em, 1001.43em, 4.219em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.741em; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-42" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">169</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(0.809em, 1001.62em, 1.243em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.299em; 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: border-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: 1.615em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.057em; 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><span class="mo" id="MathJax-Span-43" style="background-color: white; border: 0px; box-sizing: border-box; color: #333333; display: inline; font-family: MathJax_Main; font-size: 16.128px; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mstyle" face=""Source Sans Pro", "Trebuchet MS", Tahoma, sans-serif" id="MathJax-Span-44" style="background-color: white; border: 0px; box-sizing: border-box; color: #333333; display: inline; font-size: 16.128px; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-45" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-46" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.127em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.615em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.041em, 1001em, 4.405em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.493em; padding: 0px; position: absolute; top: -4.709em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-47" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.995em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.413em, 1000.5em, 4.405em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-48" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.561em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.399em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-49" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; font-size: 11.4025px; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(3.165em, 1001.49em, 4.219em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.741em; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-50" style="border: 0px; box-sizing: border-box; display: inline; font-family: MathJax_Main; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">144</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(0.809em, 1001.62em, 1.243em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.299em; 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: border-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: 1.615em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.057em; 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><span class="mo" id="MathJax-Span-51" style="background-color: white; border: 0px; box-sizing: border-box; color: #333333; display: inline; font-family: MathJax_Main; font-size: 16.128px; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-52" style="background-color: white; border: 0px; box-sizing: border-box; color: #333333; display: inline; font-family: MathJax_Main; font-size: 16.128px; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;">1</span></div><div style="text-align: justify;"><div>a) (5, 0) e (-5, 0).</div><div>b) (0, 5) e (0, -5).</div><div>c) (4, 0) e (-4, 0).</div><div>d) (3, 0) e (-3, 0).</div><div>e) Nenhuma das alternativas acima.</div><div><br /></div><span><a name='more'></a></span><div><br /></div><div><div style="background-color: white;"><div style="font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: A</b></span></div></div></div></div><div><p style="box-sizing: border-box; color: #666666; font-family: Cambria; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px;"><span style="font-family: georgia;">Dado a elipse </span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px; text-align: center;"><span style="font-family: georgia;"><span class="mstyle" face=""Source Sans Pro", "Trebuchet MS", Tahoma, sans-serif" id="MathJax-Span-36" style="border: 0px; box-sizing: border-box; color: #333333; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-37" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-38" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.127em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.615em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.041em, 1001em, 4.219em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.493em; padding: 0px; position: absolute; top: -4.709em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-39" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.995em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.413em, 1000.5em, 4.219em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-40" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.561em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.399em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-41" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(3.165em, 1001.43em, 4.219em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.741em; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-42" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">169</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(0.809em, 1001.62em, 1.243em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.299em; 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: border-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: 1.615em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.057em; 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><span class="mo" id="MathJax-Span-43" style="border: 0px; box-sizing: border-box; color: #333333; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mstyle" face=""Source Sans Pro", "Trebuchet MS", Tahoma, sans-serif" id="MathJax-Span-44" style="border: 0px; box-sizing: border-box; color: #333333; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-45" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-46" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.127em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.615em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.041em, 1001em, 4.405em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.493em; padding: 0px; position: absolute; top: -4.709em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-47" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.995em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.413em, 1000.5em, 4.405em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-48" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.561em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.399em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-49" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(3.165em, 1001.49em, 4.219em, -999.997em); left: 13.0208px; line-height: normal; margin: 0px 0px 0px -0.741em; padding: 0px; position: absolute; top: -3.345em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-50" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">144</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(0.809em, 1001.62em, 1.243em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.299em; 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: border-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: 1.615em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.057em; 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><span class="mo" id="MathJax-Span-51" style="border: 0px; box-sizing: border-box; color: #333333; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-52" style="border: 0px; box-sizing: border-box; color: #333333; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; text-align: start; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px;">1</span></span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px;"><span style="font-family: georgia;">Se:</span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px; text-align: center;"><span style="font-family: georgia;"><span face=""Source Sans Pro", "Trebuchet MS", Tahoma, sans-serif" style="border: 0px; box-sizing: border-box; color: #333333; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; text-align: left; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: 0px; width: 5.831em;"><span style="border: 0px; box-sizing: border-box; clip: rect(0.561em, 1005.77em, 3.227em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -2.291em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-54" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mstyle" id="MathJax-Span-55" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-56" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-57" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.127em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.119em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.041em, 1001em, 4.219em, -999.997em); left: 9.02083px; line-height: normal; margin: 0px 0px 0px -0.493em; padding: 0px; position: absolute; top: -4.709em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-58" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.995em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.413em, 1000.5em, 4.219em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-59" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">x</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.561em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.399em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-60" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(3.103em, 1000.93em, 4.219em, -999.997em); left: 9.02083px; line-height: normal; margin: 0px 0px 0px -0.493em; padding: 0px; position: absolute; top: -3.283em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-61" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.933em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.413em, 1000.5em, 4.219em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-62" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">a</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.561em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.337em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-63" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(0.809em, 1001.12em, 1.243em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.299em; 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: border-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: 1.119em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.057em; 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><span class="mo" id="MathJax-Span-64" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">+</span><span class="mstyle" id="MathJax-Span-65" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-66" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-67" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px 0.127em; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 1.119em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.041em, 1001em, 4.405em, -999.997em); left: 9.02083px; line-height: normal; margin: 0px 0px 0px -0.493em; padding: 0px; position: absolute; top: -4.709em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-68" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.995em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.413em, 1000.5em, 4.405em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-69" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">y<span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1px; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0.003em;"></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.561em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.399em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-70" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(3.103em, 1000.87em, 4.219em, -999.997em); left: 9.02083px; line-height: normal; margin: 0px 0px 0px -0.431em; padding: 0px; position: absolute; top: -3.283em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="msubsup" id="MathJax-Span-71" style="border: 0px; box-sizing: border-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: border-box; display: inline-block; height: 0px; line-height: normal; margin: 0px; padding: 0px; position: relative; transition: none 0s ease 0s; vertical-align: 0px; width: 0.871em;"><span style="border: 0px; box-sizing: border-box; clip: rect(3.165em, 1000.44em, 4.219em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.027em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mi" face="MathJax_Math-italic" id="MathJax-Span-72" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">b</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; left: 0.437em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -4.337em; transition: none 0s ease 0s; vertical-align: 0px;"><span class="mn" id="MathJax-Span-73" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px;">2</span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 4.033em; 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: border-box; clip: rect(0.809em, 1001.12em, 1.243em, -999.997em); left: 0em; line-height: normal; margin: 0px; padding: 0px; position: absolute; top: -1.299em; 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: border-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: 1.119em;"></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 1.057em; 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><span class="mo" id="MathJax-Span-74" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">=</span><span class="mn" id="MathJax-Span-75" style="border: 0px; box-sizing: border-box; display: inline; line-height: normal; margin: 0px; padding: 0px 0px 0px 0.251em; position: static; transition: none 0s ease 0s; vertical-align: 0px;">1</span></span><span style="border: 0px; box-sizing: border-box; display: inline-block; height: 2.297em; line-height: normal; margin: 0px; padding: 0px; position: static; transition: none 0s ease 0s; vertical-align: 0px; width: 0px;"></span></span></span><span face=""Source Sans Pro", "Trebuchet MS", Tahoma, sans-serif" 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: border-box; color: #333333; display: inline-block; height: 2.712em; line-height: normal; margin: 0px; overflow: hidden; padding: 0px; position: static; text-align: left; text-wrap: nowrap; transition: none 0s ease 0s; vertical-align: -0.899em; width: 0px;"></span></span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px;"><span style="font-family: georgia;">Temos então: a² = 169 ⇒ a = 13 e b² = 144 ⇒ b = 12.</span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="font-family: georgia;"><span style="color: #666666;">Sempre que a > b</span><span style="color: #666666;">, os focos da elipse estarão sobre o eixo x.</span></span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="color: #666666; font-family: georgia;">Vejamos as figuras a seguir.</span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://asfacesmatematica.blogspot.com/" style="margin-left: 1em; margin-right: 1em;" target="_blank"><span style="font-family: georgia;"><img border="0" data-original-height="481" data-original-width="959" height="338" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4aUNPr6I74ZDd4aPBor4aGmYVDKVRmLeQQ59pxrjIv_d3Qpif2t1EAEvwCFxV0hrUW2UM-WjdOo6g7xyNmf3FWp-X8m3QOup-Y4a1HQUfPA2KTGI14VS1UHTHxa4CEA9eTv-ZJeTloVzk1LHJ7Vp-9HRQPJ38NnYTJFSCxRfeWeMtO-TKggk2-x7MTgnI/w674-h338/PMil.png" width="674" /></span></a></div><p></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="font-family: georgia;"><span style="color: #666666;">Aplicando </span><span style="color: #666666;">Pitágoras temos:</span></span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="color: #666666; font-family: georgia;">13² = 12² + c²</span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="color: #666666; font-family: georgia;">c² = 169 − 144</span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="color: #666666; font-family: georgia;"></span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="font-family: georgia;"><span style="color: #666666;">c² = 25 </span><span style="color: #666666;">⇒ c = 5</span></span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="color: #666666; font-family: georgia;">As coordenadas dos focos são (5, 0), (-5, 0).</span></p></div></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-33571518539536078152024-02-04T17:13:00.000-08:002024-02-04T17:13:44.719-08:00(FAMEMA 2024) - QUESTÃO<div style="text-align: justify;">Seja f : <b>R</b> → <b>R</b>, definida por f(x) = x² – 2x – 24.
Considerando-se no plano cartesiano de eixos ortogonais
os pontos que representam os intersectos do gráfico dessa
função com o eixo x, a distância entre eles é igual a</div><div style="text-align: justify;">a) 4,5. </div><div style="text-align: justify;">b) 2. </div><div style="text-align: justify;">c) 6. </div><div style="text-align: justify;">d) 10. </div><div style="text-align: justify;">e) 8,5. </div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: D</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">1) Para encontrar os intersectos do gráfico de f(x)
com o eixo x, basta resolver a equação f(x) = 0. </p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">f(x) = 0 ⇒ x² – 2x – 24 = 0 ⇔ x = 6 ou x = –4</p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">2) Os intersectos de f(x) com o eixo x são os pontos
(–4; 0) e (6; 0), cuja distância é 6 + 4 = 10.</p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-74510605855023691052024-02-03T14:52:00.000-08:002024-02-03T14:52:29.074-08:00(FAMEMA 2024) - QUESTÃO<div style="text-align: justify;">O número de anagramas distintos da palavra FAMEMA
que começam e terminam com uma mesma letra é </div><div style="text-align: justify;">a) 20. </div><div style="text-align: justify;">b) 28. </div><div style="text-align: justify;">c) 8. </div><div style="text-align: justify;">d) 12. </div><div style="text-align: justify;">e) 24.</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: E</b></span></div></div></div></div><div style="background-color: white;"><p style="box-sizing: border-box; color: #666666; font-family: Cambria; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; font-family: Cambria; font-size: 16px; margin: 0px 0px 10px;">Como os anagramas devem começar e terminar com
a mesma letra, temos: </p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="font-family: Cambria;"><u><span style="color: red;">A</span></u><span style="color: #666666;"> F M E M </span><span style="color: red;"><u>A</u></span><span style="color: #666666;"> </span></span><span style="color: #202124; font-family: "Google Sans", arial, sans-serif; font-size: 14px; text-align: left;">⇒ </span><span style="color: #666666; font-family: Cambria;">4!/21 = 4.3 = 12</span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="font-family: Cambria;"><u><span style="color: red;">M</span></u><span style="color: #666666;"> F A E A </span><u><span style="color: red;">M</span></u><span style="color: #666666;"> </span></span><span style="color: #202124; font-family: "Google Sans", arial, sans-serif; font-size: 14px; text-align: left;">⇒ </span><span style="color: #666666; font-family: Cambria;">4!/2! = 4.3 = 12</span></p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="color: #666666; font-family: Cambria;">Total = 12 + 12 = 24 </span>anagramas</p><p style="box-sizing: border-box; margin: 0px 0px 10px;"><span style="font-family: Cambria;"><span style="color: #666666;"><br /></span></span></p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-88565095112867173382024-02-03T13:19:00.000-08:002024-02-03T13:19:26.139-08:00(Albert Einstein 2024) - QUESTÃO<div style="text-align: justify;">Pedro possui R$ 80.000,00, valor exato para a compra de
um carro à vista. A concessionária que vende o carro
também oferece o seguinte plano de pagamento, a prazo:
entrada de R$ 50.000,00 no ato da compra e retirada do
carro, R$ 16.000,00 após um mês da retirada do carro e
R$ 15.000,00 após dois meses da retirada do carro. Os
R$ 80.000,00 de Pedro estão aplicados em um
investimento que rende 1% ao mês, com data de
aniversário da aplicação no mesmo dia em que ele
pretende comprar o carro. Tal investimento permite
retiradas de quaisquer valores a qualquer momento. Se
Pedro optar pelo pagamento a prazo, deixando sempre o
máximo possível do seu dinheiro na aplicação financeira,
ele </div><div style="text-align: justify;">a) perderá exatamente R$ 397,00 em relação ao valor à
vista. </div><div style="text-align: justify;">b) perderá exatamente R$ 557,00 em relação ao valor à
vista. </div><div style="text-align: justify;">c) perderá exatamente R$ 608,00 em relação ao valor à
vista. </div><div style="text-align: justify;">d) ganhará exatamente R$ 557,00 em relação ao valor à
vista. </div><div style="text-align: justify;">e) ganhará exatamente R$ 608,00 em relação ao valor à
vista. </div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: B</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">1) No ato da compra, Pedro paga 50.000 reais e
aplica os outros 30.000 reais a uma taxa de 1% ao
mês. </p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">2) Um mês após a compra, após pagar a parcela de
16.000 reais, Pedro ficará com: </p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">(1,01 . 30.000 – 16.000) reais = (30.300 – 16.000) reais = 14.300 reais. </p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">3) Dois meses após a compra, depois de pagar a
parcela de 15.000 reais, Pedro ficará com: </p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">(1,01 . 14.300 – 15.000) reais = (14.443 – 15.000) reais = –557 reais.</p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-56848763984010928762024-02-03T13:16:00.000-08:002024-02-03T13:16:20.425-08:00(Albert Einstein 2024) - QUESTÃO<div style="text-align: justify;">Uma loja tem em estoque geladeiras das marcas A, B e C,
na proporção de 40%, 20% e 40%, respectivamente.
Sabe-se que 1% das geladeiras da marca A, 1% das
geladeiras da marca B e 5% das geladeiras da marca C,
em estoque, estão com defeito de fabricação. Sabe-se que
Mariana comprou uma geladeira do estoque dessa loja, e
ela estava com defeito. A probabilidade de que a geladeira
comprada por ela tenha sido da marca B é de</div><div style="text-align: justify;">a) 3/13</div><div style="text-align: justify;">b) 99/487</div><div style="text-align: justify;">c) 1/13</div><div style="text-align: justify;">d) 1/400</div><div style="text-align: justify;">e) 1/26</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px; text-align: justify;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: C</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px; text-align: justify;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><br /></p></div><div style="text-align: justify;">- A probabilidade de Mariana ter comprado uma
geladeira com defeito é: </div><div style="text-align: justify;">1% . 40% + 1% . 20% + 5% . 40% = 0,004 + 0,002 + 0,020 = 0,026</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">- A probabilidade da geladeira ser defei tuosa ser da
marca B é:</div><div style="text-align: justify;">1% . 20% = 0,002 </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">- A possibilidade pedida é 0,002/0,026 = 2/26 = 1/13</div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-85299498488384866622024-02-03T13:09:00.000-08:002024-02-03T13:10:32.338-08:00(Albert Einstein 2024) - QUESTÃO<div style="text-align: justify;">Sendo x a medida positiva de um ângulo em graus, o me -
nor valor de x que satisfaz a equação 2cos²x + 3senx = 0
é</div><div style="text-align: justify;"><div>a) 120°</div><div>b) 180°</div><div>c) 135°</div><div>d) 210°</div><div>e) 240</div><div><br /></div><span><a name='more'></a></span><div><br /></div><div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: D</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">1) cos²x = 1 – sen²x</p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">2) 2 cos²x + 3 senx = 0 ⇔ 2 (1 – sen²x) + 3 senx = 0 ⇔ –2 sen²x + 3 senx + 2 = 0 </p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">⇔ 2 sen²x – 3 senx – 2 = 0 ⇔ senx = 2 (não convém) ou senx = – 1/2</p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">Assim o menor valor de x que satisfaz a equação é 210° </p></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-40515326452607345872023-11-14T15:52:00.000-08:002023-11-14T15:52:37.564-08:00(Mackenzie - 2023) - QUESTÃO<div style="text-align: justify;">Seiscentos docinhos serão colocados em 12 bandejas de
tamanhos diferentes para serem servidos na festa de
aniversário da Melissa. A aniversariante deseja que as
quantidades de docinhos nas bandejas formem uma
progressão aritmética de razão 4. Nessas condições, a
bandeja com menor número de docinhos terá </div><div style="text-align: justify;">a) 24 docinhos. </div><div style="text-align: justify;">b) 28 docinhos. </div><div style="text-align: justify;">c) 36 docinhos. </div><div style="text-align: justify;">d) 48 docinhos. </div><div style="text-align: justify;">e) 50 docinhos. </div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: B</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">Seja “a” o menor número de docinhos e a progressão
aritmética de primeiro termo a e a razão 4. </p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px;"><span style="font-size: 16px;">1) a</span><span style="font-size: xx-small;">1</span> = a e a<span style="font-size: xx-small;">12</span> = a + 11 . 4 = a + 44</p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px;">2) [(a + a + 44) . 12]/2 = 600 ⇔ 2a + 44 = 100 ⇔ 2a = 56 ⇔ a = 28</p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-33608294305308136322023-11-14T15:49:00.000-08:002023-11-14T15:49:06.347-08:00(Mackenzie - 2023) - QUESTÃO<div style="text-align: justify;">Valentina acompanhou o crescimento de uma planta a
partir de 4cm de altura e verificou que a planta havia
dobrado de altura a cada quinzena até completar 6 quinzenas. A partir daí, o crescimento foi de 5cm por
quinzena. Então, após 10 quinzenas desde o início da
medição, a altura da planta será de </div><div style="text-align: justify;">a) 128cm </div><div style="text-align: justify;">b) 200cm </div><div style="text-align: justify;">c) 256cm </div><div style="text-align: justify;">d) 276cm </div><div style="text-align: justify;">e) 300cm</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: D</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">1) Até completar 6 quinzenas, a altura da planta, em
cm, é <span style="font-family: Cambria, serif; font-size: 12pt;">4 . 2</span><sup style="font-family: Cambria, serif;">6</sup><span style="font-family: Cambria, serif; font-size: 12pt;"> = 256.</span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">2) Após 10 quinzenas desde o início da medição, a
altura da planta será, em cm.
256 + 4 . 5 = 276</p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-75989826708992041802023-11-14T15:41:00.000-08:002023-11-14T15:41:20.349-08:00(Mackenzie - 2023) - QUESTÃO<div style="text-align: justify;">A casquinha de sorvete tem a forma de um cone. Se a
altura e a geratriz desse cone medem, respectivamente,
12cm e 13cm, então a área da superfície da casquinha,
em cm², é</div><div style="text-align: justify;">a) 25π </div><div style="text-align: justify;">b) 60π </div><div style="text-align: justify;">c) 65π </div><div style="text-align: justify;">d) l00π </div><div style="text-align: justify;">e) 156π </div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: C</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><br /></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">Seja R, em cm, o raio do cone
</p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">1) R² + (12cm)² = (13cm)² ⇒ R = 5cm </p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">2) A área, em cm², da superfície do cone (casquinha
do sorvete) é
π.R.g = π.5cm.13cm = 65πcm². </p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-54411978191851061472023-11-14T15:36:00.000-08:002023-11-14T15:36:26.921-08:00(Mackenzie - 2023) - QUESTÃO<div style="text-align: justify;">Na equação mx² – 4x – 16 = 0 temos uma raiz de valor
–2. O valor da outra raiz é </div><div style="text-align: justify;">a) –1 </div><div style="text-align: justify;">b) 1 </div><div style="text-align: justify;">c) 2 </div><div style="text-align: justify;">d) 3 </div><div style="text-align: justify;">e) 4
</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: E</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;"><br /></span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;">1) Se –2 é raiz da equação, então
m(–2)² – 4 . (–2) – 16 = 0 ⇔ 4m + 8 – 16 = 0 ⇔ 4m = 8 ⇔ m = 2.</p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px;"><span style="font-size: 16px;">2) Seja V = {–2; x</span><span style="font-size: xx-small;">2</span>} o conjunto solução da equação </p></div></div><div style="text-align: justify;">2x² – 4x – 16 = 0 e assim –2 + x<span style="font-size: xx-small;">2</span> = –(–4)/2 ⇔ x<span style="font-size: xx-small;">2</span> = 4</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">- O valor da outra raiz é 4</div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-33841745714656351542023-04-03T20:04:00.006-07:002023-04-03T20:04:51.183-07:00(UFSCAR) - QUESTÃO <div style="text-align: justify;">As funções f e g associam, a cada número natural, o
resto da divisão do número por 3 e por 6, respectivamente. Sendo assim, para todo número natural x,
g(f(x)) é igual a </div><div style="text-align: justify;">a) f(x). </div><div style="text-align: justify;">b) g(x). </div><div style="text-align: justify;">c) 2.f(x). </div><div style="text-align: justify;">d) 2.g(x). </div><div style="text-align: justify;">e) f(x) + g(x). </div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: A</b></span></div></div></div></div><div style="font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;"><br /></span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;">1) f(x) é o resto da divisão do número natural x por 3,
portanto, f(x) = 0, f(x) = 1 ou f(x) = 2. </span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;">2) g(x) é o resto da divisão do número natural x por 6,
resultando g(0) = 0, g(1) = 1 e g(2) = 2. </span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;">3) Se f(x) = 0, então g(f(x)) = g(0) = 0 = f(x). </span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;">4) Se f(x) = 1, então g(f(x)) = g(1) = 1 = f(x). </span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;">5) Se f(x) = 2, então g(f(x)) = g(2) = 2 = f(x).
Assim, g(f(x)) = f(x) para todo x natural.</span></p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-26660608712524377762023-03-26T20:22:00.004-07:002023-03-26T20:22:27.677-07:00(Furg-RS) - QUESTÃO<div style="text-align: left;">O produto de todas as raízes da equação |x² − 8| − 4 = 0 é:</div><div style="text-align: left;"><div>a) 4 </div><div>b) −4 </div><div>c) −8 </div><div>d) −48 </div><div>e) 48</div><div><br /></div><span><a name='more'></a></span><div><br /></div><div><div style="font-family: Cambria; font-size: 19.8px; text-align: justify;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: E</b></span></div></div></div></div><div style="font-family: Cambria; font-size: 19.8px; text-align: justify;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0XQCJhCaxIOSKJzoL778dMu3RP6mt7Zv7dBWmRDKIhTrmvt6Syd2ON_v8BiFiuOtpzodgriPXuyF5J7xkQov3V3dlmUIFN35icjmNrrzLExfW5w4UNIXPvNfCnWhqsDM02EmtXKmSSeMIdC89WGJUks1j7CHrBjSXYiOmS1MfNm4Zg9lruZl-qsKFxg/s666/PROMIL.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="289" data-original-width="666" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0XQCJhCaxIOSKJzoL778dMu3RP6mt7Zv7dBWmRDKIhTrmvt6Syd2ON_v8BiFiuOtpzodgriPXuyF5J7xkQov3V3dlmUIFN35icjmNrrzLExfW5w4UNIXPvNfCnWhqsDM02EmtXKmSSeMIdC89WGJUks1j7CHrBjSXYiOmS1MfNm4Zg9lruZl-qsKFxg/s16000/PROMIL.png" /></a></div></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-56235912636978021212023-03-26T19:55:00.000-07:002023-03-26T19:55:06.579-07:00(EEM-SP) - QUESTÃO<div style="text-align: justify;">Uma função satisfaz a relação
f(2x) = 2f(x) + f(2), para qualquer valor real de x.
Sabendo-se que f(4) = 6, calcule f(16).</div><div style="text-align: justify;"><div>a) 28</div><div>b) 30</div><div>c) 32</div><div>d) 37</div><div>e) 40</div></div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white;"><div style="font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: B</b></span></div></div></div></div><div><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">Fazendo x = 2, vem:</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(2.2) = 2f(2) + f(2)</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(4) = 3f(2)</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">6 = 3f(2)</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(2) = 2</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">Fazendo x = 4, vem:</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(8) = 2f(4) + f(2)</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(8) = 2.6 + 2</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(8) = 14</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">Fazendo x = 8, vem:</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(16) = 2f(8) + f(2)</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(16) = 28 + 2</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: georgia;">f(16) = 30</span></p></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-82658503468550512902023-01-27T17:15:00.004-08:002023-01-27T17:16:37.348-08:00(FUVEST 2023) - QUESTÃO<div style="text-align: justify;">Para medir o volume de uma pedra com formato irregular, Ana utilizou um recipiente cilíndrico de raio r = 8 cm e com água até a altura de 20 cm. Após colocar a pedra no recipiente, a altura da água subiu para 23,5 cm.</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMYrrRhkMGngEDiNI3MgSxamdzOvISnea1VHZ41Lh3akg7l9LN9tcjxw5DK_DsK0AqMtiTzcwTpES4wHvzMfSnqtu5G7EztXOpzE2Ec75pOElSHFTzHSz_erzTV_nyW10l2PEL-xd8iv7CselDliA0_cbMtpDM_FMBBacIzOYlNvTFtQc2AtS0vvvIGg/s373/FDM.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="263" data-original-width="373" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMYrrRhkMGngEDiNI3MgSxamdzOvISnea1VHZ41Lh3akg7l9LN9tcjxw5DK_DsK0AqMtiTzcwTpES4wHvzMfSnqtu5G7EztXOpzE2Ec75pOElSHFTzHSz_erzTV_nyW10l2PEL-xd8iv7CselDliA0_cbMtpDM_FMBBacIzOYlNvTFtQc2AtS0vvvIGg/s16000/FDM.jpg" /></a></div><div style="text-align: justify;">O volume da pedra é: </div><div style="text-align: justify;"><div>a) 128π cm³ </div><div>b) 224π cm³ </div><div>c) 240π cm³ </div><div>d) 282π cm³ </div><div>e) 320π cm³</div></div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: B</b></span></div></div></div></div><div style="background-color: white; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;">Após colocar a pedra no recipiente, a altura da água passa de 20 cm para 23,5 cm. O volume da pedra (V) é igual ao volume de um cilindro cujo raio da base é igual a 8 cm e altura igual a:</span></p><p align="center" style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px;"><span style="font-family: georgia;">23,5 cm – 20 cm = 3,5 cm</span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;">Assim, teremos:</span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;">V = <span style="font-size: medium; text-align: justify;">π.8².3,5</span></span></p><p style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;">V = 224<span style="font-size: medium; text-align: justify;">π.cm³</span></span></p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-14083097244408428562023-01-27T16:59:00.002-08:002023-01-27T17:15:48.008-08:00(FUVEST 2023) - QUESTÃO<div style="text-align: justify;">Um professor precisa elaborar uma prova multidisciplinar que consta de duas questões de Matemática e seis de Física. Ele deve escolher questões de um banco de dados que contém três questões de Matemática e oito de Física. O número de provas distintas possíveis, sem levar em conta a ordem em que as questões aparecem, é: </div><div style="text-align: justify;"><div>a) 42 </div><div>b) 54 </div><div>c) 62 </div><div>d) 72 </div><div>e) 84</div><div><br /></div><span><a name='more'></a></span><div><br /></div><div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: E</b></span></div></div></div></div><div style="background-color: white;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;"><span style="color: #666666; font-size: 16px;">A partir do banco de dados disponível, que possui 3 questões de matemática e 8 de física, é preciso que se escolham 2 questões de matemática dentre estas 3, e 6 questões de física dentre estas 8. Isso pode ser feito de C</span><span style="color: #666666;"><span style="font-size: xx-small;">3,2</span></span><span style="color: #666666; font-size: 16px;">.C</span><span style="color: #666666;"><span style="font-size: xx-small;">8,3</span></span><span style="color: #666666; font-size: 16px;"> </span></span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;"><span style="color: #666666; font-size: 16px;">C</span><span style="color: #666666;"><span style="font-size: xx-small;">3,2</span></span><span style="color: #666666; font-size: 16px;">. </span><span style="color: #666666; font-size: 16px;">= 3!/2!(3 - 2)! = 3</span></span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;"><span style="color: #666666; font-size: 16px;">C</span><span style="color: #666666;"><span style="font-size: xx-small;">8,3</span></span><span style="color: #666666; font-size: 16px;"> = 8!/6!(8 - 6)! = 28</span></span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="font-family: georgia;"><span style="color: #666666; font-size: 16px;">C</span><span style="color: #666666;"><span style="font-size: xx-small;">3,2</span></span><span style="color: #666666; font-size: 16px;">.C</span><span style="color: #666666;"><span style="font-size: xx-small;">8,3 </span></span><span style="color: #666666; font-size: 16px;">= 3.28 = 84</span><span style="color: #666666; font-size: 16px;"> </span><span style="color: #666666; font-size: 16px;"> maneiras.</span></span></p></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-18183823600605588662023-01-27T16:50:00.005-08:002023-01-27T16:52:44.409-08:00(FUVEST 2023) - QUESTÃO<div style="text-align: justify;"><div>No plano cartesiano, os pontos (3, 2) e (5, 4) pertencem ao gráfico da função dada por y = log<span style="font-size: xx-small;">2</span>(ax + b).</div><div>O valor de a + b é: </div><div>a) - 8 </div><div>b) - 6 </div><div>c) 0 </div><div>d) 4 </div><div>e) 8</div><div><br /></div><span><a name='more'></a></span><div><br /></div><div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: A</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px;">Do enunciado, obtém-se o sistema:</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"></p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBzWxS6xDeFAwgWrEvLkZ-RIR8yH8iDO-pknMuRlj0pC4VeHkLJhowhNtHF7opWM8VMo9UquzYuSp5jWX74vcuhtXuRSKnmrCfUQzTJDkrJW14naUjhcEP42NetQgZtlsPaBpV39sSciTN5hTGphYTG8frnbzwIZNT0GKBMMFuUsklXu750UCo17dPjA/s773/C+S.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="243" data-original-width="773" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBzWxS6xDeFAwgWrEvLkZ-RIR8yH8iDO-pknMuRlj0pC4VeHkLJhowhNtHF7opWM8VMo9UquzYuSp5jWX74vcuhtXuRSKnmrCfUQzTJDkrJW14naUjhcEP42NetQgZtlsPaBpV39sSciTN5hTGphYTG8frnbzwIZNT0GKBMMFuUsklXu750UCo17dPjA/s16000/C+S.png" /></a></div><br /><span style="color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px;"><br /></span><p></p></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-11541611128958180112023-01-27T16:45:00.001-08:002023-01-27T16:45:14.001-08:00(FUVEST 2023) - QUESTÃO<div style="text-align: justify;">Em uma feira de produtos orgânicos é vendido arroz a granel. A gerente da feira decidiu oferecer descontos progressivos na venda de arroz, de acordo com os seguintes critérios:</div><div style="text-align: justify;">• Quem comprar exatamente 1 kg de arroz paga R$ 5,00.</div><div style="text-align: justify;">• Quanto maior for a quantidade que o cliente comprar, maior será o total a pagar.</div><div style="text-align: justify;">• Quanto maior for a quantidade que o cliente comprar, menor será o valor por quilo.</div><div style="text-align: justify;">Cada uma das alternativas listadas apresenta uma possível fórmula para o total que o cliente irá pagar, em reais, se comprar uma quantidade x, em quilos, de arroz. A única alternativa que atende aos critérios estabelecidos é:</div><div style="text-align: justify;">a) 5x²</div><div style="text-align: justify;">b) 5√x</div><div style="text-align: justify;">c) 5/x</div><div style="text-align: justify;">d) 5x</div><div style="text-align: justify;">e) 5x - x²</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: B</b></span></div></div></div></div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">Das informações dadas no enunciado, devemos ter uma função y = f(x) tal que</p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><span style="font-size: 12px;">• </span>f(1) = 5</p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><span style="bottom: -0.25em; box-sizing: border-box; font-size: 12px; line-height: 0; position: relative; vertical-align: baseline;">• </span>f é crescente;</p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><span style="bottom: -0.25em; box-sizing: border-box; font-size: 12px; line-height: 0; position: relative; vertical-align: baseline;">• </span>f possui crescimento cada vez mais lento.</p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">Dentre as opções apresentadas, a única que possui essas características é f(x) = 5√x.</p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-40305798204472640682023-01-27T16:38:00.005-08:002023-01-27T16:38:46.644-08:00(FUVEST 2023) - QUESTÃO<div style="text-align: justify;">Joana comprou um celular e dividiu o pagamento em 24 parcelas mensais que formam uma progressão aritmética crescente. As três primeiras parcelas foram de R$ 120,00, R$ 126,00 e R$ 132,00. Sabendo que, ao final, constatou-se que Joana não pagou a 19ª parcela, o valor pago por ela foi:</div><div style="text-align: justify;"><div>a) R$ 3.954,00 </div><div>b) R$ 4.026,00 </div><div>c) R$ 4.200,00 </div><div>d) R$ 4.308,00 </div><div>e) R$ 4.382,00</div><div><br /></div><span><a name='more'></a></span><div><br /></div><div><div style="font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: D</b></span></div></div></div></div><div><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"><span style="color: #666666; font-family: PT Sans, Helvetica, Arial;">Calculando:</span></p><p class="rtejustify" style="box-sizing: border-box; margin: 0px 0px 10px; text-align: start;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTj09Vi7z4eVrYtflcqW2M9hNY94rpjc4HS16hxNgnUdkkk8QoBDj4ayGoa3LbD4Ajb4kNVNvhGCdEzjuGzwpOIq_k_n2bASpc_3x44Pxl0npw53Bf7ZX9QRZg1sKuF9DotJ2Pe15WdkJVjRQQj_3s2PAxmT9LHF9rij6PidGLa-4nufy-3z8CgaEIIg/s719/C+S.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="334" data-original-width="719" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTj09Vi7z4eVrYtflcqW2M9hNY94rpjc4HS16hxNgnUdkkk8QoBDj4ayGoa3LbD4Ajb4kNVNvhGCdEzjuGzwpOIq_k_n2bASpc_3x44Pxl0npw53Bf7ZX9QRZg1sKuF9DotJ2Pe15WdkJVjRQQj_3s2PAxmT9LHF9rij6PidGLa-4nufy-3z8CgaEIIg/s16000/C+S.png" /></a></div><p></p></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-18908873607967459572023-01-27T16:24:00.003-08:002023-01-27T16:24:24.133-08:00(FGV-SP 2023) - QUESTÃO<div style="text-align: justify;"><div>O número de anagramas da palavra COMUM nos quais as duas letras M não aparecem juntas é</div><div>a) 18</div><div>b) 24</div><div>c) 36</div><div>d) 48</div><div>e) 60</div><div><br /></div><span><a name='more'></a></span><div><div style="background-color: white; font-size: 19.8px;"><div style="font-size: 19.8px;"><div style="font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: C</b></span></div></div></div></div><div style="font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-size: 16px; margin: 0px 0px 10px; text-align: justify;"><span style="font-family: georgia;">Existem 5!/2! = 60 anagramas da palavra COMUM. Destes, considerando as duas letras M como uma única escolha, tem-se 4! = 24 anagramas em que as duas letras M aparecem juntas. Assim, existem 60 – 24 = 36 anagramas nos quais as duas letras M não aparecem juntas.</span></p></div></div></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-42724170670998369052023-01-27T16:21:00.006-08:002023-01-27T16:21:53.684-08:00(FGV-SP 2023) - QUESTÃO<div style="text-align: justify;">Certo produto é transportado em contêineres cúbicos. Para reduzir o custo da embalagem no transporte, os transportadores pretendem trocar o contêiner atual por um cubo maior, com aresta duas vezes a aresta do cubo atual. Suponha que o material gasto para montar um contêiner seja proporcional à área da superfície do cubo. Ao transportar um volume correspondente ao cubo maior totalmente cheio, a economia de material com o cubo maior em relação ao material gasto com os contêineres atuais, necessários para transportar o mesmo volume, é de</div><div style="text-align: justify;"><div>a) 10%</div><div>b) 20%</div><div>c) 30%</div><div>d) 40%</div><div>e) 50%</div><div><br /></div><span><a name='more'></a></span><div><div style="background-color: white;"><div><div style="font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: E</b></span></div></div></div></div><div><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px; text-align: justify;"><span style="font-family: georgia;">Sendo x a medida da aresta do cubo que representa um dos contêineres atuais, a medida da aresta do cubo maior é 2x. Como a medida da aresta do cubo maior é o dobro da medida da aresta do cubo menor, então o volume do cubo maior será 2<span style="box-sizing: border-box; line-height: 0; position: relative; top: -0.5em; vertical-align: baseline;">³</span> = 8 vezes o volume do cubo menor.</span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px; text-align: justify;"><span style="font-family: georgia;">Desta forma, o material gasto para transportar um volume no cubo maior é proporcional a 6.(2x)² = 24x² e o material gasto para transportar esse mesmo volume nos cubos menores é proporcional a 8.6x² = 48x².</span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px; text-align: justify;"><span style="font-family: georgia;">Assim, a economia de material em relação ao material gasto com os contêineres atuais é de </span></p><p style="box-sizing: border-box; color: #666666; margin: 0px 0px 10px; text-align: justify;"><span style="font-family: georgia;"><span style="bottom: -0.25em; box-sizing: border-box; line-height: 0; position: relative; vertical-align: baseline;">(24x² - 48x²)/48x² = - 24x²/48x² = - 50% </span>.</span></p></div></div></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-82986929271428872742023-01-27T16:16:00.001-08:002023-01-27T16:16:01.383-08:00(FGV-SP 2023) - QUESTÃO<div style="text-align: justify;">Em uma certa loja, uma camisa que custava R$ 150,00 teve o seu preço aumentado em um certo percentual e, a seguir, esse novo preço foi diminuído do mesmo percentual resultando em um preço final de R$ 126,00.</div><div style="text-align: justify;">O percentual citado foi de</div><div style="text-align: justify;">a) 24% </div><div style="text-align: justify;">b) 25% </div><div style="text-align: justify;">c) 30% </div><div style="text-align: justify;">d) 36% </div><div style="text-align: justify;">e) 40%</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div style="font-size: 19.8px;"><div style="font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: E</b></span></div></div></div></div><div style="font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">Sendo p o percentual citado, temos:</p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">150.(1 + p).(1 - p) = 126</p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">1 - p² = 0,84</p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">p² = 0,16</p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">p = 0,4 = 40%</p></div></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-63629228547602450112023-01-27T16:11:00.004-08:002023-01-27T16:11:30.889-08:00(FGV-SP 2023) - QUESTÃO<div style="text-align: justify;">João emitiu uma nota fiscal de R$ 2000,00. O comprador se espantou, dizendo que não era esse o preço original combinado. João então explicou que o preço combinado não considerava o imposto e que 20% do valor da nota fiscal emitida era imposto.</div><div style="text-align: justify;">Quanto João acrescentou de imposto ao preço original combinado com o comprador, em termos percentuais?</div><div style="text-align: justify;">a) 18%</div><div style="text-align: justify;">b) 25%</div><div style="text-align: justify;">c) 20%</div><div style="text-align: justify;">d) 27%</div><div style="text-align: justify;">e) 22%</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div style="font-size: 19.8px;"><div style="font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: B</b></span></div></div></div></div><div style="font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">O imposto corresponde a 20% de R$ 2.000,00, ou seja, R$ 400,00. Dessa forma, o preço original combinado era de R$ 2.000,00 – R$ 400,00 = R$ 1.600,00.</p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">Esse imposto de R$ 400,00 representa, em relação ao preço combinado: R$ 400,00/R$ 1.600,00 = 25%</p></div></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-81516142534035674992023-01-27T16:07:00.003-08:002023-01-27T16:07:12.884-08:00(FGV-SP 2023) - QUESTÃO<div style="text-align: justify;">Dados dois pontos A(a, b) e B(c, d) em um sistema de coordenadas cartesianas, definimos a “distância do taxista” entre os pontos A e B, representada por d(A, B), como sendo <b>d(A, B) = |a - c| + |b - d|</b></div><div style="text-align: justify;">A distância do taxista para ir do ponto A(−3, 2) ao ponto B(1, −2) e a seguir do ponto B ao ponto C(4, 3) é</div><div style="text-align: justify;"><div>a) 13</div><div>b) 14</div><div>c) 15</div><div>d) 16</div><div>e) 17</div><div><br /></div><span><a name='more'></a></span><div><br /></div><div><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div style="font-size: 19.8px;"><div style="font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: D</b></span></div></div></div></div><div style="font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;">Temos:</span></p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;">d(A, B) = |</span><span style="color: black; font-family: "Times New Roman"; font-size: medium;">− </span><span style="text-align: start;">3 </span><span style="color: black; font-family: "Times New Roman"; font-size: medium;">−</span><span style="text-align: start;"> 1| + |2 </span><span style="color: black; font-family: "Times New Roman"; font-size: medium;">−</span><span style="text-align: start;"> (</span><span style="color: black; font-family: "Times New Roman"; font-size: medium;">−</span><span style="text-align: start;">2)| </span></p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;">d(A, B) = 4 + 4 = 8</span></p><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;">d(B, C) = |1 </span><span style="font-family: "Times New Roman"; font-size: medium;">− 4| + |</span><span style="font-family: "Times New Roman"; font-size: medium;">− 2 </span><span style="font-family: "Times New Roman"; font-size: medium;">− 3| = 3 + 5 = 8</span></p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">Dessa forma, a distância total é 8 + 8 = 16.</p></div></div></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-48667686006929621102023-01-27T16:00:00.001-08:002023-01-27T16:00:53.841-08:00(FGV-SP 2023) - QUESTÃO<div style="text-align: justify;">O primeiro termo de uma progressão aritmética é a<span style="font-size: xx-small;">1</span> = 1, e a média dos 2021 primeiros termos é 102. A razão desta progressão aritmética é</div><div style="text-align: justify;">a) 0,10</div><div style="text-align: justify;">b) 0,15</div><div style="text-align: justify;">c) 0,20</div><div style="text-align: justify;">d) 0,25</div><div style="text-align: justify;">e) 0,30</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="font-family: Cambria; font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: A</b></span></div></div></div></div><div style="font-family: Cambria; font-size: 19.8px;"><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheE779S12u5Ptrueefds4PpTLAa3GmdohEGlLQQyw-vHIrKrTCw_RcL6rWFl9WY88C-uFw7gPMhtvXn7CaCOgEFzqvQwYDsbnh34yHtBqgfCmMkS_HQYG8y3ir17obi4DQ941ren1P_x9GoPCYVhH_-IBzfAFOpIAyWVsuCNUdT_M5OG05FLZIdgIZrQ/s736/C+S.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="492" data-original-width="736" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheE779S12u5Ptrueefds4PpTLAa3GmdohEGlLQQyw-vHIrKrTCw_RcL6rWFl9WY88C-uFw7gPMhtvXn7CaCOgEFzqvQwYDsbnh34yHtBqgfCmMkS_HQYG8y3ir17obi4DQ941ren1P_x9GoPCYVhH_-IBzfAFOpIAyWVsuCNUdT_M5OG05FLZIdgIZrQ/s16000/C+S.png" /></a></div><br /><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><br /></p></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0tag:blogger.com,1999:blog-1940576058607823274.post-44400252436678255012023-01-27T15:56:00.002-08:002023-01-27T15:57:21.164-08:00(FGV-SP 2023) - QUESTÃO<div style="text-align: justify;">No plano cartesiano, a área do triângulo delimitado pelas retas 5x − 3y + 1 = 0 , y − 2 = 0 e 5x + y − 27 = 0 é</div><div style="text-align: justify;">a) 27</div><div style="text-align: justify;">b) 15 </div><div style="text-align: justify;">c) 12</div><div style="text-align: justify;">d) 10 </div><div style="text-align: justify;">e) 8</div><div style="text-align: justify;"><br /></div><span><a name='more'></a></span><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><div style="background-color: white; font-family: Cambria; font-size: 19.8px;"><div style="font-size: 19.8px;"><div class="post-body entry-content" id="post-body-5130806679783503333" itemprop="description articleBody" style="font-size: 21.78px; line-height: 1.4; position: relative; text-align: start; width: 720px;"><div dir="ltr"><div class="post-footer" style="background-color: #fff2cc; border-bottom: 1px solid rgba(0, 0, 0, 0); color: #444444; font-size: 19.602px; line-height: 1.6; margin: 20px -2px 0px; padding: 5px 10px;"><span style="font-family: courier;"><b>Resolução: D</b></span></div></div></div></div><div style="font-size: 19.8px;"><p style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px;"><span style="text-align: start;"><br /></span></p><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;">Vamos determinar as coordenadas de cada vértice:</p><div class="separator" style="clear: both; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8vLC4I1SyN393jTqr8csJFp9idS_R1K1pUp7dz59otl7YfCiQCWWOZvLn_FmRs8itbr5DmQkafqLD0DZgI50uezIpGVP4mkrP6IQ2mH76ruAn-J0ibfbdsq4K0PvWlf0qa8vnBdSZOaOrmrZ-nfb-m6OeYVrdze0XILpvwzwuDp2kd7qH3-44LbVaRQ/s797/C+S.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="661" data-original-width="797" height="615" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8vLC4I1SyN393jTqr8csJFp9idS_R1K1pUp7dz59otl7YfCiQCWWOZvLn_FmRs8itbr5DmQkafqLD0DZgI50uezIpGVP4mkrP6IQ2mH76ruAn-J0ibfbdsq4K0PvWlf0qa8vnBdSZOaOrmrZ-nfb-m6OeYVrdze0XILpvwzwuDp2kd7qH3-44LbVaRQ/w741-h615/C+S.png" width="741" /></a></div><br /><p class="rtejustify" style="box-sizing: border-box; color: #666666; font-family: "PT Sans", Helvetica, Arial; font-size: 16px; margin: 0px 0px 10px; text-align: start;"><br /></p></div></div></div>Espaço do estudantehttp://www.blogger.com/profile/03136249799925393618noreply@blogger.com0