{"id":6464,"date":"2011-02-01T02:46:03","date_gmt":"2011-02-01T02:46:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6464"},"modified":"2022-01-18T00:57:55","modified_gmt":"2022-01-18T00:57:55","slug":"pinheiros-de-natal","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6464","title":{"rendered":"Pinheiros de Natal"},"content":{"rendered":"<p><ul id='GTTabs_ul_6464' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6464' class='GTTabs_curr'><a  id=\"6464_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6464' ><a  id=\"6464_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_6464'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6465\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6465\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\" data-orig-size=\"503,407\" 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=\"Pinheiro de Natal\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\" class=\"alignright wp-image-6465 size-full\" title=\"Pinheiro de Natal\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\" alt=\"\" width=\"503\" height=\"407\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg 503w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3-300x242.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3-150x121.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3-400x323.jpg 400w\" sizes=\"auto, (max-width: 503px) 100vw, 503px\" \/>O Bernardo \u00e9 escuteiro e organizou uma venda de pinheiros de Natal. Em vez de uma lista de pre\u00e7os, afixou o gr\u00e1fico representado abaixo.<\/p>\n<ol>\n<li>Comenta a seguinte afirma\u00e7\u00e3o: &#8220;O Bernardo decidiu que o pre\u00e7o dos pinheiros deve ser diretamente proporcional \u00e0 respetiva altura.&#8221;<\/li>\n<li>Determina a express\u00e3o anal\u00edtica que indica o pre\u00e7o em fun\u00e7\u00e3o da altura.<\/li>\n<li>O pinheiro de Natal comprado pela Junta de Freguesia da terra do Bernardo custou 9 euros. Qual \u00e9 a altura do pinheiro?<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\">\u00a0<\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6464' onClick='GTTabs_show(1,6464)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6464'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6465\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6465\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\" data-orig-size=\"503,407\" 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=\"Pinheiro de Natal\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\" class=\"alignright wp-image-6465 size-full\" title=\"Pinheiro de Natal\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg\" alt=\"\" width=\"503\" height=\"407\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3.jpg 503w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3-300x242.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3-150x121.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8-pag71-3-400x323.jpg 400w\" sizes=\"auto, (max-width: 503px) 100vw, 503px\" \/><\/a>O gr\u00e1fico que representa a correspond\u00eancia entre a altura dos pinheiros e o seu custo \u00e9 um conjunto de pontos pertencentes a uma reta que passa na origem do referencial. Logo, a rela\u00e7\u00e3o entre as grandezas (altura e custo) \u00e9 de proporcionalidade direta.<br \/>\n\u00ad<\/li>\n<li>A constante de proporcionalidade \u00e9 $k=\\frac{2}{50}=\\frac{4}{100}=&#8230;=\\frac{12}{300}=0,04$ (\u20ac\/cm).<br \/>\nA express\u00e3o anal\u00edtica pedida pode ser $c=0,04\\times h$, designando c o custo em euros e h a altura do pinheiro em cent\u00edmetros.<br \/>\n\u00ad<\/li>\n<li>Substituindo na equa\u00e7\u00e3o anterior a vari\u00e1vel c por 9 (euros), obtemos: $9=0,04\\times h$.<br \/>\nResolvendo esta equa\u00e7\u00e3o, temos: \\[\\begin{array}{*{35}{l}}<br \/>\n9=0,04\\times h &amp; \\Leftrightarrow\u00a0 &amp; 0,04\\times h=9\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; h=\\frac{9}{0,04}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; h=225\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nA altura do pinheiro \u00e9 225 cm, ou seja, 2,25 m.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6464' onClick='GTTabs_show(0,6464)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Bernardo \u00e9 escuteiro e organizou uma venda de pinheiros de Natal. Em vez de uma lista de pre\u00e7os, afixou o gr\u00e1fico representado abaixo. Comenta a seguinte afirma\u00e7\u00e3o: &#8220;O Bernardo decidiu&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20567,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,127],"tags":[128,130],"series":[],"class_list":["post-6464","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-funcoes","tag-funcoes-2","tag-proporcionalidade-directa"],"views":2438,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/8V1Pag071-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6464","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=6464"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6464\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20567"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6464"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6464"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6464"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6464"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}