{"id":6492,"date":"2011-02-25T00:44:28","date_gmt":"2011-02-25T00:44:28","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6492"},"modified":"2022-01-22T00:16:41","modified_gmt":"2022-01-22T00:16:41","slug":"nivel-de-alcool-no-sangue","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6492","title":{"rendered":"N\u00edvel de \u00e1lcool no sangue"},"content":{"rendered":"<p><ul id='GTTabs_ul_6492' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6492' class='GTTabs_curr'><a  id=\"6492_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6492' ><a  id=\"6492_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_6492'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Pretende-se esbo\u00e7ar o gr\u00e1fico de N, que d\u00e1 o &#8220;N\u00edvel de \u00e1lcool no sangue&#8221;, em fun\u00e7\u00e3o do peso p de uma pessoa, depois de ela ter ingerido um litro de cerveja.<\/p>\n<p>Sabe-se que:<\/p>\n<ul>\n<li>num litro de cerveja existem 40 g de \u00e1lcool;<\/li>\n<li>N(p) \u00e9 a raz\u00e3o entre o peso (em gramas) de \u00e1lcool existente no litro de cerveja e o volume (em litros) do fluido org\u00e2nico da pessoa;<\/li>\n<li>o volume de l\u00edquido org\u00e2nico de cada pessoa \u00e9 numericamente igual a 70% do seu peso total (em quilogramas).<\/li>\n<\/ul>\n<p>Sabendo que N(p) \u00e9 expresso em gramas por litro e p \u00e9 expresso em quilogramas,<\/p>\n<ol>\n<li>determine N(30), N(60) e N(80);<\/li>\n<li>esboce o gr\u00e1fico de N, quando p varia der 20 a 130;<\/li>\n<li>em Portugal, a lei estabelece penas avultadas para quem for apanhado a conduzir com um n\u00edvel de \u00e1lcool no sangue superior a 0,5 gramas por litro.<br \/>\nIndique, nas condi\u00e7\u00f5es do enunciado, quem n\u00e3o deve conduzir depois de beber um litro de cerveja.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6492' onClick='GTTabs_show(1,6492)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6492'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como $N(p)=\\frac{40}{0,7p}$, temos:<br \/>\n$N(30)=\\frac{40}{0,7\\times 30}\\approx 1,90$ (g\/l);<br \/>\n$N(60)=\\frac{40}{0,7\\times 60}\\approx 0,95$ (g\/l)<br \/>\ne $N(80)=\\frac{40}{0,7\\times 80}\\approx 0,71$ (g\/l).<br \/>\n\u00ad<\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6493\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6493\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-1.jpg\" data-orig-size=\"198,134\" 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=\"J1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-1.jpg\" class=\"alignnone size-full wp-image-6493\" title=\"J1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-1.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-1.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-1-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6494\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6494\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-2.jpg\" data-orig-size=\"198,134\" 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=\"G1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-2.jpg\" class=\"alignnone size-full wp-image-6494\" title=\"G1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-2.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-2.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-2-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><br \/>\n\u00ad<\/li>\n<li>Nas condi\u00e7\u00f5es do enunciado, depois de beber um litro de cerveja n\u00e3o devem conduzir pessoas com menos\u00a0 de 114 kg, aproximadamente:\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6495\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6495\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-3.jpg\" data-orig-size=\"198,134\" 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=\"G2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-3.jpg\" class=\"alignnone size-full wp-image-6495\" title=\"G2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-3.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-3.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-12-3-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><\/p>\n<p>Analiticamente, temos (note que $p&gt;0$):<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\nN(p)&gt;0,5 &amp; \\Leftrightarrow\u00a0 &amp; \\frac{40}{0,7p}&gt;0,5\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; 0,35p&lt;40\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; p&lt;\\frac{40}{0,35}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; p&lt;\\frac{800}{7}\u00a0 \\\\<br \/>\n\\end{array}\\]Note que $\\frac{800}{7}\\approx 114,29$.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6492' onClick='GTTabs_show(0,6492)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Pretende-se esbo\u00e7ar o gr\u00e1fico de N, que d\u00e1 o &#8220;N\u00edvel de \u00e1lcool no sangue&#8221;, em fun\u00e7\u00e3o do peso p de uma pessoa, depois de ela ter ingerido um litro de cerveja.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20856,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,125],"tags":[131],"series":[],"class_list":["post-6492","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-racionais","tag-funcoes-racionais-2"],"views":3097,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11V2Pag185-12_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6492","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=6492"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6492\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20856"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6492"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}