{"id":6515,"date":"2011-02-25T17:10:20","date_gmt":"2011-02-25T17:10:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6515"},"modified":"2022-01-22T00:25:39","modified_gmt":"2022-01-22T00:25:39","slug":"um-aquario-aberto-em-cima","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6515","title":{"rendered":"Um aqu\u00e1rio aberto em cima"},"content":{"rendered":"<p><ul id='GTTabs_ul_6515' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6515' class='GTTabs_curr'><a  id=\"6515_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6515' ><a  id=\"6515_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6515'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um aqu\u00e1rio aberto em cima, de forma paralelepip\u00e9dica, com 45 cm de altura, deve ter o volume de 170 litros.<\/p>\n<p>Sejam x e y o comprimento e a largura da base, respetivamente.<\/p>\n<ol>\n<li>Exprima y como fun\u00e7\u00e3o de x.<\/li>\n<li>Exprima, em fun\u00e7\u00e3o de x, a \u00e1rea total do vidro necess\u00e1rio.<\/li>\n<li>Determine um valor de x, aproximado \u00e0s d\u00e9cimas, para o qual essa \u00e1rea \u00e9 m\u00ednima.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6515' onClick='GTTabs_show(1,6515)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6515'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como $170\\,l=170\\,d{{m}^{3}}$, operando em dec\u00edmetros, temos:<br \/>\n\\[4,5xy=170\\Leftrightarrow y=\\frac{170}{4,5x}\\]<\/li>\n<li>A\u00a0 \u00e1rea total de vidro necess\u00e1rio, em cent\u00edmetros quadrados, pode ser expressa por:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nA(x) &amp; = &amp; x\\times \\frac{170}{4,5x}+2\\times x\\times 4,5+2\\times \\frac{170}{4,5x}\\times 4,5\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\frac{170}{4,5}+9x+\\frac{340}{x}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 9x+\\frac{340}{9}+\\frac{340}{x}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/li>\n<li>A \u00e1rea de vidro necess\u00e1rio \u00e9 m\u00ednima para $x=61,5$ (cm), aproximadamente:\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6517\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6517\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap1.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"J1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap1.jpg\" class=\"alignnone size-full wp-image-6517\" title=\"J1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap1.jpg\" alt=\"\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap1.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap1-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6518\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6518\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap2.jpg\" data-orig-size=\"264,136\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"G1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap2.jpg\" class=\"alignnone size-full wp-image-6518\" title=\"G1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap2.jpg\" alt=\"\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap2.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/DispCap2-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6515' onClick='GTTabs_show(0,6515)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um aqu\u00e1rio aberto em cima, de forma paralelepip\u00e9dica, com 45 cm de altura, deve ter o volume de 170 litros. Sejam x e y o comprimento e a largura da base,&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20858,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,125],"tags":[131],"series":[],"class_list":["post-6515","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-racionais","tag-funcoes-racionais-2"],"views":3428,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11V2Pag187-18_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6515","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6515"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6515\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20858"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6515"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6515"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6515"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6515"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}