{"id":7200,"date":"2011-11-26T21:38:25","date_gmt":"2011-11-26T21:38:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7200"},"modified":"2022-01-25T22:30:33","modified_gmt":"2022-01-25T22:30:33","slug":"servico-na-urgencia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7200","title":{"rendered":"Servi\u00e7o na Urg\u00eancia"},"content":{"rendered":"<p><ul id='GTTabs_ul_7200' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7200' class='GTTabs_curr'><a  id=\"7200_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7200' ><a  id=\"7200_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_7200'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Todos os m\u00e9dicos que est\u00e3o de servi\u00e7o na Urg\u00eancia se cumprimentaram apertando a m\u00e3o.<\/p>\n<p>Sabendo que foram dados 45 apertos de m\u00e3o, quantos m\u00e9dicos est\u00e3o de servi\u00e7o?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7200' onClick='GTTabs_show(1,7200)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7200'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>A pessoa A n\u00e3o se cumprimenta a si pr\u00f3pria e o cumprimento entre as pessoas A e B \u00e9 \u00fanico.<\/p>\n<p>Trata-se, portanto, de determinar $n$, tal que $^{n}{{C}_{2}}=45$.<\/p>\n<p>Ora, $$\\begin{array}{*{35}{l}}<br \/>\n^{n}{{C}_{2}}=45 &amp; \\Leftrightarrow\u00a0 &amp; \\begin{matrix}<br \/>\n\\frac{n(n-1)(n-2)!}{(n-2)\\times 2!}=45 &amp; \\wedge\u00a0 &amp; n\\in \\mathbb{N}\u00a0 \\\\<br \/>\n\\end{matrix}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\begin{matrix}<br \/>\n\\frac{n(n-1)}{2}=45 &amp; \\wedge\u00a0 &amp; n\\in \\mathbb{N}\u00a0 \\\\<br \/>\n\\end{matrix}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\begin{matrix}<br \/>\n{{n}^{2}}-n-90=0 &amp; \\wedge\u00a0 &amp; n\\in \\mathbb{N}\u00a0 \\\\<br \/>\n\\end{matrix}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\begin{matrix}<br \/>\nn=\\frac{1\\mp \\sqrt{1+360}}{2} &amp; \\wedge\u00a0 &amp; n\\in \\mathbb{N}\u00a0 \\\\<br \/>\n\\end{matrix}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\begin{matrix}<br \/>\n(n=10\\vee n=-9) &amp; \\wedge\u00a0 &amp; n\\in \\mathbb{N}\u00a0 \\\\<br \/>\n\\end{matrix}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; n=10\u00a0 \\\\<br \/>\n\\end{array}$$<\/p>\n<p>Portanto, est\u00e3o dez m\u00e9dicos de servi\u00e7o.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7200' onClick='GTTabs_show(0,7200)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Todos os m\u00e9dicos que est\u00e3o de servi\u00e7o na Urg\u00eancia se cumprimentaram apertando a m\u00e3o. Sabendo que foram dados 45 apertos de m\u00e3o, quantos m\u00e9dicos est\u00e3o de servi\u00e7o? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt;&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21037,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255],"series":[],"class_list":["post-7200","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-probabilidades-e-combinatoria","tag-12-o-ano","tag-analise-combinatoria"],"views":1678,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/12V1Pag174-45_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7200","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=7200"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7200\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21037"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7200"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7200"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7200"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}