{"id":14556,"date":"2018-04-15T16:09:18","date_gmt":"2018-04-15T15:09:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14556"},"modified":"2022-01-07T22:41:24","modified_gmt":"2022-01-07T22:41:24","slug":"um-reservatorio-de-oleo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14556","title":{"rendered":"Um reservat\u00f3rio de \u00f3leo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14556' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14556' class='GTTabs_curr'><a  id=\"14556_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14556' ><a  id=\"14556_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_14556'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>O n\u00edvel <em>N<\/em> de \u00f3leo (em litros) de um reservat\u00f3rio varia com o tempo <em>t<\/em> (em horas), de acordo com a express\u00e3o:<\/p>\n<p>\\[N\\left( t \\right) = &#8211; 0,6\\,{t^2} + 0,25\\,t + 0,7\\]<\/p>\n<ol>\n<li>No in\u00edcio da contagem do tempo, havia \u00f3leo no reservat\u00f3rio?<br \/>\nExplica a tua resposta.<\/li>\n<li>Ao fim de quanto tempo o n\u00edvel de \u00f3leo \u00e9 zero?<br \/>\nApresenta esse valor em horas e minutos arredondados \u00e0 unidade.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14556' onClick='GTTabs_show(1,14556)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14556'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>O n\u00edvel <em>N<\/em> de \u00f3leo (em litros) de um reservat\u00f3rio varia com o tempo <em>t<\/em> (em horas), de acordo com a express\u00e3o:<\/p>\n<p>\\[N\\left( t \\right) = &#8211; 0,6\\,{t^2} + 0,25\\,t + 0,7\\]<\/p>\n<\/blockquote>\n<ol>\n<li>No in\u00edcio da contagem do tempo, havia 0,7 litros de \u00f3leo no reservat\u00f3rio, pois \\(N\\left( 0 \\right) = &#8211; 0,6 \\times {0^2} + 0,25 \\times 0 + 0,7 = 0,7\\).<br \/>\n\u00ad<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{N\\left( t \\right) = 0}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{ &#8211; 0,6\\,{t^2} + 0,25\\,t + 0,7 = 0}&amp; \\wedge &amp;{t &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{60\\,{t^2} &#8211; 25\\,t &#8211; 70 = 0}&amp; \\wedge &amp;{t &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{t = \\frac{{25 \\mp \\sqrt {625 + 16800} }}{{120}}}&amp; \\wedge &amp;{t &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{t = \\frac{{25 \\mp 5\\sqrt {697} }}{{120}}}&amp; \\wedge &amp;{t &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{t = \\frac{{5 \\mp \\sqrt {697} }}{{24}}}&amp; \\wedge &amp;{t &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{t = \\frac{{5 &#8211; \\sqrt {697} }}{{24}}}&amp; \\vee &amp;{t = \\frac{{5 + \\sqrt {697} }}{{24}}}\\end{array}} \\right)}&amp; \\wedge &amp;{t &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{t = \\frac{{5 + \\sqrt {697} }}{{24}}}\\\\{}&amp;{}&amp;{t \\approx 1,308365}\\end{array}\\]<br \/>\nO n\u00edvel de \u00f3leo \u00e9 zero, aproximadamente, ao fim de 1 hora e 19 minutos, ap\u00f3s o in\u00edcio da contagem de tempo.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14556' onClick='GTTabs_show(0,14556)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O n\u00edvel N de \u00f3leo (em litros) de um reservat\u00f3rio varia com o tempo t (em horas), de acordo com a express\u00e3o: \\[N\\left( t \\right) = &#8211; 0,6\\,{t^2} + 0,25\\,t +&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14558,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,160,304],"series":[],"class_list":["post-14556","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-equacoes-do-2-o-grau","tag-9-o-ano","tag-equacao","tag-formula-resolvente"],"views":3330,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag94-6a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14556","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=14556"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14556\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14558"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14556"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}