{"id":14483,"date":"2018-04-14T12:52:50","date_gmt":"2018-04-14T11:52:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14483"},"modified":"2022-01-07T21:53:00","modified_gmt":"2022-01-07T21:53:00","slug":"uma-caixa-cubica-sem-tampa","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14483","title":{"rendered":"Uma caixa c\u00fabica sem tampa"},"content":{"rendered":"<p><ul id='GTTabs_ul_14483' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14483' class='GTTabs_curr'><a  id=\"14483_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14483' ><a  id=\"14483_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_14483'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14484\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14484\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\" data-orig-size=\"270,245\" 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=\"Caixa\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\" class=\"alignright size-full wp-image-14484\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\" alt=\"\" width=\"270\" height=\"245\" \/><\/a>A medida da aresta de uma caixa c\u00fabica \u00e9 <em>x<\/em> dm.<\/p>\n<p>Sabendo que a \u00e1rea total da superf\u00edcie da caixa \u00e9 125 dm<sup>2<\/sup>, qual \u00e9 o valor de x?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14483' onClick='GTTabs_show(1,14483)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14483'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14484\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14484\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\" data-orig-size=\"270,245\" 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=\"Caixa\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\" class=\"alignright size-full wp-image-14484\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13.png\" alt=\"\" width=\"270\" height=\"245\" \/><\/a>Em fun\u00e7\u00e3o de <em>x<\/em>, a \u00e1rea total da superf\u00edcie da caixa pode ser expressa por:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{A_T}}&amp; = &amp;{5 \\times {A_{Face}}}\\\\{}&amp; = &amp;{5 \\times {x^2}}\\\\{}&amp; = &amp;{5{x^2}}\\end{array}\\]<\/p>\n<p>Como\u00a0a \u00e1rea total da superf\u00edcie da caixa \u00e9 125 dm<sup>2<\/sup>, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{A_T} = 125}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{5{x^2} = 125}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{x^2} = 25}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{\\left( {\\begin{array}{*{20}{c}}{x = &#8211; 5}&amp; \\vee &amp;{x = 5}\\end{array}} \\right)}&amp; \\wedge &amp;{x &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{x = 5}\\end{array}\\]<\/p>\n<p>Portanto,\u00a0\\({x = 5}\\).<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14483' onClick='GTTabs_show(0,14483)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A medida da aresta de uma caixa c\u00fabica \u00e9 x dm. Sabendo que a \u00e1rea total da superf\u00edcie da caixa \u00e9 125 dm2, qual \u00e9 o valor de x? Resolu\u00e7\u00e3o &gt;&gt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14485,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,303],"tags":[426,108,306],"series":[],"class_list":["post-14483","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-area","tag-equacao-do-2-o-grau"],"views":2741,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag89-13a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14483","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=14483"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14483\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14485"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14483"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14483"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14483"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}