{"id":11729,"date":"2014-02-01T21:58:41","date_gmt":"2014-02-01T21:58:41","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11729"},"modified":"2022-01-22T01:17:57","modified_gmt":"2022-01-22T01:17:57","slug":"uma-plataforma-petrolifera","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11729","title":{"rendered":"Uma plataforma petrol\u00edfera"},"content":{"rendered":"<p><ul id='GTTabs_ul_11729' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11729' class='GTTabs_curr'><a  id=\"11729_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11729' ><a  id=\"11729_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_11729'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Para construir uma plataforma petrol\u00edfera, o custo aproximado por tonelada \u00e9 dado, em euros, para $x$ mil toneladas, por:<\/p>\n<p>\\[C\\left( x \\right) = \\frac{{312000,5}}{{x + 625}}\\]<\/p>\n<ol>\n<li>Qual \u00e9 o custo por tonelada para $30$ mil toneladas?<\/li>\n<li>Quantas mil toneladas tem a plataforma, se o custo por tonelada foi de $483$ euros?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11729' onClick='GTTabs_show(1,11729)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11729'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora, \u00a0$C\\left( {30} \\right) = \\frac{{312000,5}}{{30 + 625}} = \\frac{{312000,5}}{{655}} \\approx 476,34$.<br \/>\nPara $30$ mil toneladas, \u00a0o custo por tonelada \u00e9 $476,34$ \u20ac, aproximadamente.<br \/>\n\u00ad<\/li>\n<li>Tem-se sucessivamente:<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{C\\left( x \\right) = 843}&amp; \\Leftrightarrow &amp;{\\frac{{312000,5}}{{x + 625}} = 483} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\frac{{312000,5 &#8211; 483x &#8211; 301875}}{{x + 625}} = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\frac{{10125,5 &#8211; 483x}}{{x + 625}} = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{10125,5 &#8211; 483x}&amp; \\wedge &amp;{x + 625 \\ne 0}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = \\frac{{2893}}{{138}}} \\\\<br \/>\n{}&amp;{}&amp;{x \\approx 21}<br \/>\n\\end{array}\\]<br \/>\nSe o custo por tonelada foi de $483$ euros, a plataforma tem, aproximadamente, $21$ mil toneladas.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11729' onClick='GTTabs_show(0,11729)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Para construir uma plataforma petrol\u00edfera, o custo aproximado por tonelada \u00e9 dado, em euros, para $x$ mil toneladas, por: \\[C\\left( x \\right) = \\frac{{312000,5}}{{x + 625}}\\] Qual \u00e9 o custo por&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20867,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,125],"tags":[422,160,126],"series":[],"class_list":["post-11729","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-racionais","tag-11-o-ano","tag-equacao","tag-funcao-racional"],"views":2201,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/02\/11V2Pag48-5_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11729","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=11729"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11729\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20867"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11729"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}