{"id":6482,"date":"2011-02-24T22:11:50","date_gmt":"2011-02-24T22:11:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6482"},"modified":"2022-01-22T00:09:14","modified_gmt":"2022-01-22T00:09:14","slug":"uma-unidade-industrial","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6482","title":{"rendered":"Uma unidade industrial"},"content":{"rendered":"<p><ul id='GTTabs_ul_6482' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6482' class='GTTabs_curr'><a  id=\"6482_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6482' ><a  id=\"6482_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_6482'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>\u00a0Uma unidade industrial trata p% da \u00e1gua que lan\u00e7a ao rio.<\/p>\n<p>O custo do tratamento, C(p), \u00e9 dado em milhares de euros pela express\u00e3o \\[C(p)=\\frac{230p}{100-p}\\]<\/p>\n<ol>\n<li>Calcule o custo do tratamento de 10% da \u00e1gua.<\/li>\n<li>Apresente uma tabela de valores do custo, de 10% em 10%, e o gr\u00e1fico de C.<\/li>\n<li>Observe como varia o custo da unidade percentual. Essa varia\u00e7\u00e3o \u00e9 constante?\n<p>Apresente duas tabelas, uma com os valores de x entre 0% e 10%, de 1% em 1%, e outra de valores de x entre 90% e 100% e descreva essa varia\u00e7\u00e3o.<\/p>\n<\/li>\n<li>Se houver uma manifesta\u00e7\u00e3o a exigir que seja tratado mais 1% da \u00e1gua, fica mais dispendioso ceder aos manifestantes se j\u00e1 se tratar 20% da \u00e1gua ou se j\u00e1 se tratar 95%?<\/li>\n<li>Pode-se esperar que seja tratada a totalidade da \u00e1gua? Justifique.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6482' onClick='GTTabs_show(1,6482)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6482'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora, $C(10)=\\frac{230\\times 10}{100-10}=\\frac{2300}{90}\\approx 25,556$.<br \/>\nO tratamento de 10% da \u00e1gua tem o custo de 25.556 \u20ac, aproximadamente.<br \/>\n\u00ad<\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6483\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6483\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-1.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=\"T1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-1.jpg\" class=\"size-full wp-image-6483 alignnone\" title=\"T1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-1.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-1.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-1-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6484\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6484\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-2.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-pag182-2-2.jpg\" class=\"size-full wp-image-6484 alignnone\" title=\"G1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-2.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-2.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-2-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><br \/>\n\u00ad<\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6485\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6485\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-3.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=\"T2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-3.jpg\" class=\"alignnone size-full wp-image-6485\" title=\"T2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-3.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-3.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-3-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-4.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6486\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6486\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-4.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=\"T3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-4.jpg\" class=\"alignnone size-full wp-image-6486\" title=\"T3\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-4.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-4.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-4-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a><br \/>\nA varia\u00e7\u00e3o do custo da unidade percentual n\u00e3o \u00e9 constante, aumenta com o aumento da percentadem da \u00e1gua tratada.<br \/>\n\u00ad<\/li>\n<li>Fica bastante mais dispendioso se j\u00e1 se tratar 95% da \u00e1gua:\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-5.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6487\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6487\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-5.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=\"T4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-5.jpg\" class=\"alignnone size-full wp-image-6487\" title=\"T4\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-5.jpg\" alt=\"\" width=\"198\" height=\"134\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-5.jpg 198w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11-pag182-2-5-150x101.jpg 150w\" sizes=\"auto, (max-width: 198px) 100vw, 198px\" \/><\/a>\u00ad<\/p>\n<\/li>\n<li>N\u00e3o, pois $p=100$ n\u00e3o pertence ao dom\u00ednio da fun\u00e7\u00e3o.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6482' onClick='GTTabs_show(0,6482)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado \u00a0Uma unidade industrial trata p% da \u00e1gua que lan\u00e7a ao rio. O custo do tratamento, C(p), \u00e9 dado em milhares de euros pela express\u00e3o \\[C(p)=\\frac{230p}{100-p}\\] Calcule o custo do tratamento de&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20854,"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-6482","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-funcoes-racionais","tag-funcoes-racionais-2"],"views":2367,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/02\/11V2Pag182-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6482","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=6482"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6482\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20854"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6482"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}