{"id":14506,"date":"2018-04-14T22:01:42","date_gmt":"2018-04-14T21:01:42","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14506"},"modified":"2022-01-07T22:09:48","modified_gmt":"2022-01-07T22:09:48","slug":"a-temperatura-de-um-forno","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14506","title":{"rendered":"A temperatura de um forno"},"content":{"rendered":"<p><ul id='GTTabs_ul_14506' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14506' class='GTTabs_curr'><a  id=\"14506_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14506' ><a  id=\"14506_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_14506'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-18.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14508\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14508\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-18.png\" data-orig-size=\"250,245\" 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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Forno\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-18.png\" class=\"alignright size-full wp-image-14508\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-18.png\" alt=\"\" width=\"250\" height=\"245\" \/><\/a>A temperatura <em>C<\/em> (em graus Celcius) de um forno \u00e9 regulada de modo que varie com o tempo (em minutos) de acordo com a express\u00e3o:<\/p>\n<p>\\[C\\left( t \\right) = 150 &#8211; 0,5\\,{t^2} + 15\\,t\\]<\/p>\n<p>com\u00a0\\(0 \\le t \\le 20\\).<\/p>\n<ol>\n<li>Calcula a temperatura no instante \\(t = 0\\).<\/li>\n<li>Qual \u00e9 o instante em que a temperatura atinge o valor 202\u00ba C?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14506' onClick='GTTabs_show(1,14506)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14506'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>No\u00a0instante \\(t = 0\\), a temperatura do forno \u00e9 de \\(C\\left( 0 \\right) = 150 &#8211; 0,5 \\times {0^2} + 15 \\times 0 = 150\\) \u00ba C.<br \/>\n\u00ad<\/li>\n<li>A temperatura\u00a0atinge o valor 202\u00ba C no instante\u00a0\\({t = 4}\\):<br \/>\n\\[\\begin{array}{*{20}{l}}{C\\left( t \\right) = 202}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{150 &#8211; 0,5\\,{t^2} + 15\\,t = 202}&amp; \\wedge &amp;{0 \\le t \\le 20}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{ &#8211; 0,5\\,{t^2} + 15\\,t &#8211; 52 = 0}&amp; \\wedge &amp;{0 \\le t \\le 20}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{t = \\frac{{ &#8211; 15 \\mp \\sqrt {225 &#8211; 104} }}{{ &#8211; 1}}}&amp; \\wedge &amp;{0 \\le t \\le 20}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{t = 15 \\mp 11}&amp; \\wedge &amp;{0 \\le t \\le 20}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{t = 4}&amp; \\vee &amp;{t = 26}\\end{array}} \\right)}&amp; \\wedge &amp;{0 \\le t \\le 20}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{t = 4}\\end{array}\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14506' onClick='GTTabs_show(0,14506)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A temperatura C (em graus Celcius) de um forno \u00e9 regulada de modo que varie com o tempo (em minutos) de acordo com a express\u00e3o: \\[C\\left( t \\right) = 150 &#8211;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14507,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,306,304],"series":[],"class_list":["post-14506","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-do-2-o-grau","tag-formula-resolvente"],"views":2568,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-18a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14506","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=14506"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14506\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14507"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14506"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}