{"id":11726,"date":"2014-01-31T00:52:26","date_gmt":"2014-01-31T00:52:26","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=11726"},"modified":"2022-01-22T01:13:44","modified_gmt":"2022-01-22T01:13:44","slug":"numero-de-horas-de-estudo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=11726","title":{"rendered":"N\u00famero de horas de estudo"},"content":{"rendered":"<p><ul id='GTTabs_ul_11726' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_11726' class='GTTabs_curr'><a  id=\"11726_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_11726' ><a  id=\"11726_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_11726'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A fun\u00e7\u00e3o \\[E\\left( x \\right) = \\frac{{0,32x}}{{100,5 &#8211; x}}\\] permite determinar o n\u00famero de horas de estudo, $E\\left( x \\right)$, necess\u00e1rias para obter num teste um resultado $x$, entre $0$ e $100$ (em percentagem).<\/p>\n<ol>\n<li>Quantas horas de estudo s\u00e3o necess\u00e1rias para se obter $85$ (em percentagem)?<br \/>\nApresente o resultado em horas e minutos, com aproxima\u00e7\u00e3o ao minuto.<\/li>\n<li>Qual o resultado (com aproxima\u00e7\u00e3o \u00e0s d\u00e9cimas) que se obt\u00e9m se se estudar $8$ horas?<\/li>\n<li>Quantas horas de estudo s\u00e3o necess\u00e1rias para se obter $100$ (em percentagem)?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_11726' onClick='GTTabs_show(1,11726)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_11726'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como \\[E\\left( {85} \\right) = \\frac{{0,32 \\times 85}}{{100,5 &#8211; 85}} = \\frac{{27,2}}{{15,5}} \\approx 1,755\\] e $0,755 \\times 60 = 45,3$, para se obter $85$ (em percentagem) nesse teste, \u00e9 necess\u00e1rio um estudo de $1$ hora e $45$ minutos, aproximadamente.<br \/>\n\u00ad<\/li>\n<li>Tem-se sucessivamente:<br \/>\n\\[\\begin{array}{*{20}{l}}<br \/>\n{E\\left( x \\right) = 8}&amp; \\Leftrightarrow &amp;{\\frac{{0,32x}}{{100,5 &#8211; x}} = \\mathop 8\\limits_{\\left( {100,5 &#8211; x} \\right)} } \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\frac{{0,32x + 8x &#8211; 804}}{{100,5 &#8211; x}} = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\frac{{8,32x &#8211; 804}}{{100,5 &#8211; x}} = 0} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{8,32x &#8211; 804 = 0}&amp; \\wedge &amp;{100,5 &#8211; x \\ne 0}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{l}}<br \/>\n{x = \\frac{{804}}{{8,32}}}&amp; \\wedge &amp;{x \\ne 100,5}<br \/>\n\\end{array}} \\\\<br \/>\n{}&amp; \\Leftrightarrow &amp;{x = \\frac{{5025}}{{52}}} \\\\<br \/>\n{}&amp;{}&amp;{x \\approx 96,6}<br \/>\n\\end{array}\\]<\/p>\n<p>Se se estudar $8$ horas, obt\u00e9m-se, aproximadamente, a percentagem de ${96,6}$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>Como \\[E\\left( {100} \\right) = \\frac{{0,32 \\times 100}}{{100,5 &#8211; 100}} = \\frac{{32}}{{0,5}} = 64\\] para se obter $85$ (em percentagem) nesse teste, \u00e9 necess\u00e1rio um estudo de $64$ horas.<\/li>\n<\/ol>\n<div id=\"attachment_11728\" style=\"width: 702px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11728\" data-attachment-id=\"11728\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=11728\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4.png\" data-orig-size=\"1412,935\" 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=\"Gr\u00e1fico4\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Resolu\u00e7\u00e3o gr\u00e1fica do problema&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4-1024x678.png\" class=\" wp-image-11728  \" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4.png\" alt=\"Resolu\u00e7\u00e3o gr\u00e1fica do problema\" width=\"692\" height=\"458\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4.png 1412w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4-300x198.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4-1024x678.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4-150x99.png 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11-2pag-48-4-400x264.png 400w\" sizes=\"auto, (max-width: 692px) 100vw, 692px\" \/><\/a><p id=\"caption-attachment-11728\" class=\"wp-caption-text\">Resolu\u00e7\u00e3o gr\u00e1fica do problema<\/p><\/div>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_11726' onClick='GTTabs_show(0,11726)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A fun\u00e7\u00e3o \\[E\\left( x \\right) = \\frac{{0,32x}}{{100,5 &#8211; x}}\\] permite determinar o n\u00famero de horas de estudo, $E\\left( x \\right)$, necess\u00e1rias para obter num teste um resultado $x$, entre $0$ e&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20865,"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-11726","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":1788,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2014\/01\/11V2Pag48-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11726","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=11726"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/11726\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20865"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11726"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=11726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}