{"id":7177,"date":"2011-11-15T23:41:21","date_gmt":"2011-11-15T23:41:21","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7177"},"modified":"2022-01-15T21:41:14","modified_gmt":"2022-01-15T21:41:14","slug":"na-quinta-de-alzubar","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7177","title":{"rendered":"Na quinta de Alzubar"},"content":{"rendered":"<p><ul id='GTTabs_ul_7177' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7177' class='GTTabs_curr'><a  id=\"7177_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7177' ><a  id=\"7177_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_7177'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Para planear a apanha da uva, na quinta de Alzubar, construi-se a seguinte tabela:<\/p>\n<table class=\"aligncenter\" style=\"border: 1px solid #ffffff; width: 60%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"background-color: #ff99cc;\"><span style=\"color: #000000;\">N\u00famero de trabalhadores ($t$)<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffccff;\">100<\/td>\n<td style=\"text-align: center; background-color: #ffccff;\">50<\/td>\n<td style=\"text-align: center; background-color: #ffccff;\">25<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #ff66cc;\"><span style=\"color: #000000;\">N\u00famero de dias que leva a apanha da uva ($d$)<\/span><\/td>\n<td style=\"text-align: center; background-color: #ff99ff;\">1<\/td>\n<td style=\"text-align: center; background-color: #ff99ff;\">2<\/td>\n<td style=\"text-align: center; background-color: #ff99ff;\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/uvas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7178\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7178\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/uvas.jpg\" data-orig-size=\"379,280\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;7.1&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;Canon PowerShot A610&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1188476402&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;7.3&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0.005&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Uvas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/uvas.jpg\" class=\"alignright size-full wp-image-7178\" title=\"Uvas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/uvas.jpg\" alt=\"\" width=\"136\" height=\"101\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/uvas.jpg 379w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/uvas-300x221.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/uvas-150x110.jpg 150w\" sizes=\"auto, (max-width: 136px) 100vw, 136px\" \/><\/a>Na tabela, as vari\u00e1veis $t$ e $d$ referem-se a grandezas inversamente proporcionais.<\/p>\n<ol>\n<li>Quando o n\u00famero de trabalhadores aumenta, o que acontece ao n\u00famero de dias que leva a apanha da fruta?<\/li>\n<li>Determina a constante de proporcionalidade inversa.<\/li>\n<li>Neste caso, o que representa a constante de proporcionalidade inversa?<\/li>\n<li>Constr\u00f3i o gr\u00e1fico da situa\u00e7\u00e3o e assinala o tempo correspondente \u00e0 apanha da uva feita por 20 e por 80 trabalhadores.<\/li>\n<li>Indica a express\u00e3o que relaciona o n\u00famero de trabalhadores ($t$) com o n\u00famero de dias ($d$) necess\u00e1rio para apanhar a uva, na quinta de Alzubar.\n<p>[<strong>A<\/strong>] $100\\,t=d$\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 [<strong>B<\/strong>] $t+d=100$\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 [<strong>C<\/strong>] $\\frac{t}{d}=100$\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 [<strong>D<\/strong>] $t\\times d=100$<\/p>\n<\/li>\n<li>Na quinta de Alzubar, a apanha da uva demorou 4 dias, e foram apanhados, no total, 80.000 kg de uva.<br \/>\nEm m\u00e9dia, quantos quilogramas de uva apanhou cada trabalhador por dia?<br \/>\nExplica a tua resposta e apresenta todos os c\u00e1lculos que efetuares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7177' onClick='GTTabs_show(1,7177)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7177'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Quando o n\u00famero de trabalhadores aumenta, diminui o n\u00famero de dias que leva a apanha da fruta.<br \/>\n\u00ad<\/li>\n<li>A constante de proporcionalidade inversa \u00e9 $k=100$, pois $100\\times 1=50\\times 2=25\\times 4=100$.<br \/>\n\u00ad<\/li>\n<li>A constante de proporcionalidade corresponde ao n\u00famero de trabalhadores necess\u00e1rios para apanhar as uvas em apenas um dia.<br \/>\n\u00ad<\/li>\n<li>Para $t=20$, vem $20\\times d=100\\Leftrightarrow d=5$.<br \/>\nPara $t=80$, vem $80\\times d=100\\Leftrightarrow d=1,25$.<br \/>\nApresenta-se, seguidamente, o gr\u00e1fico pedido:<\/p>\n<p><script 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><br \/>\n\u00ad<\/p>\n<\/li>\n<li>A express\u00e3o correta \u00e9 [<strong>D<\/strong>] $t\\times d=100$.<br \/>\n\u00ad<\/li>\n<li>Em m\u00e9dia, os 25 trabalhadores apanharam $\\frac{80000}{4}=20000$ kg de uva por dia.<br \/>\nConsequentemente, em m\u00e9dia, cada um desses trabalhadores, apanhou $\\frac{20000}{25}=800$ kg de uva por dia.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7177' onClick='GTTabs_show(0,7177)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Para planear a apanha da uva, na quinta de Alzubar, construi-se a seguinte tabela: N\u00famero de trabalhadores ($t$) 100 50 25 N\u00famero de dias que leva a apanha da uva ($d$)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20292,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,249],"tags":[426,129,250],"series":[],"class_list":["post-7177","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-grafico-cartesiano","tag-proporcionalidade-inversa-2"],"views":2216,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/9V1PropInversa-NaQuintaDeAlzubar_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7177","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=7177"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7177\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20292"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7177"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}