{"id":204319,"date":"2023-10-28T06:10:32","date_gmt":"2023-10-28T09:10:32","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=204319"},"modified":"2023-10-28T06:10:32","modified_gmt":"2023-10-28T09:10:32","slug":"a-problema-de-gincana-a-altura-de-uma-mesa","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/a-problema-de-gincana-a-altura-de-uma-mesa\/","title":{"rendered":"(A) Problema de Gincana: A altura de uma mesa"},"content":{"rendered":"<p class=\"ti3\"  style=\"text-align:center;\">Clique no bot\u00e3o abaixo para visualizar o problema.<\/p>\n<div style=\"text-align:center;margin-top:10px;\">\n<input class=\"bo1 c1 cb13\" style=\"width:150px;\" value=\"Problema\" title=\"Clique aqui\" type=\"button\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Problema';}\" \/>  <\/p>\n<div style=\"display: none;\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Problema<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nObserve a figura abaixo.<\/p>\n<ul>\n<li>A dist\u00e2ncia do topo do cubo no ch\u00e3o at\u00e9 o topo do cilindro na mesa \u00e9 de [tex]1\\,\\text{m}.[\/tex]<\/li>\n<li>A dist\u00e2ncia do topo do mesmo cilindro no ch\u00e3o at\u00e9 o topo do mesmo cubo na mesma mesa \u00e9 de [tex]\\dfrac{4}{5}\\,\\text{m}[\/tex]. <\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2023\/10\/r063.png\" style=\"border: 0px ;alt=\"\" width=\"476\" height=\"187\" class=\"aligncenter size-full wp-image-203270\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2023\/10\/r063.png 476w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2023\/10\/r063-300x118.png 300w\" sizes=\"auto, (max-width: 476px) 100vw, 476px\" \/><br \/>\n<strong>Encontre a altura da mesa. D\u00ea sua resposta em metros.<\/strong><\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\nVamos denotar por [tex]x[\/tex] a altura do cilindro e por  [tex]y[\/tex] a altura do cubo. Com isso, vamos atualizar as medidas que aparecem na figura original do problema:<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2023\/10\/r063_2.png\"  style=\"border: 0px alt=\"\" width=\"510\" height=\"330\" class=\"aligncenter size-full wp-image-204305\" \/><br \/>\nObserve que temos duas express\u00f5es para a altura da mesa: [tex]\\boxed{1-x+y}~[\/tex] e [tex]~\\boxed{\\dfrac{4}{5}-y+x}[\/tex]; assim, segue que:<br \/>\n[tex]\\qquad 1-x+y=\\dfrac{4}{5}-y+x \\\\<br \/>\n\\qquad 2x-2y=\\dfrac{1}{5}\\\\<br \/>\n\\qquad  x-y=\\dfrac{1}{10}.[\/tex]<\/p>\n<p style=\"margin:10px\">\n<p>Portanto, a altura da mesa pode ser assim calculada:<br \/>\n[tex]\\qquad \\textcolor{blue}{altura}=1-x+y=1-(x-y)\\\\<br \/>\n\\qquad \\textcolor{blue}{altura}=1-\\dfrac{1}{10}\\\\<br \/>\n\\qquad \\textcolor{blue}{\\boxed{altura=\\dfrac{9}{10}\\ \\text{m}}}.[\/tex]<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"gg\">\nPrimeira Gincana de 2023 &#8211; Clubes de Matem\u00e1tica da OBMEP<br \/>\nN\u00edvel A &#8211; Quest\u00e3o Mediana<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Clique no bot\u00e3o abaixo para visualizar o problema. Problema Observe a figura abaixo. A dist\u00e2ncia do topo do cubo no ch\u00e3o at\u00e9 o topo do cilindro na mesa \u00e9 de [tex]1\\,\\text{m}.[\/tex] A dist\u00e2ncia do topo do mesmo cilindro no ch\u00e3o at\u00e9 o topo do mesmo cubo na mesma mesa \u00e9 de [tex]\\dfrac{4}{5}\\,\\text{m}[\/tex]. Observe que temos &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/a-problema-de-gincana-a-altura-de-uma-mesa\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-204319","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/204319","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=204319"}],"version-history":[{"count":1,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/204319\/revisions"}],"predecessor-version":[{"id":204320,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/204319\/revisions\/204320"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=204319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}