{"id":6565,"date":"2011-03-01T19:55:51","date_gmt":"2011-03-01T19:55:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6565"},"modified":"2022-01-23T16:39:52","modified_gmt":"2022-01-23T16:39:52","slug":"do-terraco-de-um-predio-lancou-se-uma-bola","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6565","title":{"rendered":"Do terra\u00e7o de um pr\u00e9dio lan\u00e7ou-se uma bola"},"content":{"rendered":"<p><ul id='GTTabs_ul_6565' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6565' class='GTTabs_curr'><a  id=\"6565_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6565' ><a  id=\"6565_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<li id='GTTabs_li_2_6565' ><a  id=\"6565_2\" onMouseOver=\"GTTabsShowLinks('Simula\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Simula\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_6565'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Do terra\u00e7o de um pr\u00e9dio lan\u00e7ou-se uma bola para cima. A altura a (em dec\u00e2metros), a que a bola se encontra da rua, \u00e9 dada em fun\u00e7\u00e3o do tempo (em segundos) pela express\u00e3o:<br \/>\n\\[a(t)=-0,5{{t}^{2}}+4t+4,5\\]<\/p>\n<ol>\n<li>Qual \u00e9 a altura do terra\u00e7o?<\/li>\n<li>Qual o intervalo de tempo em que a bola est\u00e1 acima dos 120 metros?<\/li>\n<li>Compare os valores da velocidade m\u00e9dia nos intervalos [0, 2] e [2, 3]. Que conclui?<\/li>\n<li>Qual \u00e9 a altura m\u00e1xima que a bola atinge? Em que instante atinge esse valor?<\/li>\n<li>Ao fim de quanto tempo cai a bola na rua? Qual \u00e9 o valor da velocidade nesse instante?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6565' onClick='GTTabs_show(1,6565)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6565'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como $a(0)=-0,5\\times {{0}^{2}}+4\\times 0+4,5=4,5$, o terra\u00e7o tem 45 metros de altura.\n<p style=\"text-align: center;\" data-tadv-p=\"keep\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-1.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6566\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6566\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-1.jpg\" data-orig-size=\"264,136\" 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=\"J1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-1.jpg\" class=\"alignnone size-full wp-image-6566\" title=\"J1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-1.jpg\" alt=\"\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-1.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-1-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6567\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6567\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-2.jpg\" data-orig-size=\"264,136\" 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\/03\/11-pag-194-37-2.jpg\" class=\"alignnone size-full wp-image-6567\" title=\"G1\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-2.jpg\" alt=\"\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-2.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-2-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><br \/>\n\u00ad<\/p>\n<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\na(t)&gt;12 &amp; \\Leftrightarrow\u00a0 &amp; -0,5{{t}^{2}}+4t+4,5&gt;12\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -0,5{{t}^{2}}+4t-7,5&gt;0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; -0,5(t-3)(t-5)&gt;0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; t\\in \\left] 3,5 \\right[\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>C\u00e1lculos auxiliares:<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\n-0,5{{t}^{2}}+4t-7,5=0 &amp; \\Leftrightarrow\u00a0 &amp; t=\\frac{-4\\mp \\sqrt{16-15}}{-1}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; t=3\\vee t=5\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>A bola est\u00e1 acima dos 120 metros entre os 3 e 5 segundos ap\u00f3s o seu lan\u00e7amento.<\/p>\n<p style=\"text-align: center;\" data-tadv-p=\"keep\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6568\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6568\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-3.jpg\" data-orig-size=\"264,136\" 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=\"G2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-3.jpg\" class=\"alignnone size-full wp-image-6568\" title=\"G2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-3.jpg\" alt=\"\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-3.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-3-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-4.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6569\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6569\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-4.jpg\" data-orig-size=\"264,136\" 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=\"G3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-4.jpg\" class=\"alignnone size-full wp-image-6569\" title=\"G3\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-4.jpg\" alt=\"\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-4.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-4-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a><br \/>\n\u00ad<\/p>\n<\/li>\n<li>Ora,<br \/>\n\\[tm{{v}_{\\left[ 0,2 \\right]}}=\\frac{(-0,5\\times {{2}^{2}}+4\\times 2+4,5)-(-0,5\\times {{0}^{2}}+4\\times 0+4,5)}{2-0}=\\frac{6}{2}=3\\]\\[tm{{v}_{\\left[ 2,3 \\right]}}=\\frac{(-0,5\\times {{3}^{2}}+4\\times 3+4,5)-(-0,5\\times {{2}^{2}}+4\\times 2+4,5)}{3-2}=12-10,5=1,5\\]<br \/>\nNo intervalo [0, 2] a velocidade m\u00e9dia \u00e9 de 30 m\/s, enquanto que no intervalo [2, 3] \u00e9 de 15 m\/s.<br \/>\nConclui-se, por isso, que entre os 2 e 3 segundos a bola sobe mais devagar do que nos dois primeiros segundos.<br \/>\n\u00ad<\/li>\n<li>A bola atinge a altura m\u00e1xima no instante em que a velocidade anular.\n<p>Como $a'(t)=-t+4$, ent\u00e3o $a'(t)=0\\Leftrightarrow -t+4=0\\Leftrightarrow t=4$.<\/p>\n<p>Dado que $a(4)=-0,5\\times {{4}^{2}}+4\\times 4+4,5=12,5$, a bola atinge a altura m\u00e1xima de 125 metros, 4 segundos ap\u00f3s o seu lan\u00e7amento.<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-5.jpg\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6570\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6570\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-5.jpg\" data-orig-size=\"264,136\" 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=\"G4\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-5.jpg\" class=\"alignnone size-full wp-image-6570 aligncenter\" title=\"G4\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-5.jpg\" alt=\"\" width=\"264\" height=\"136\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-5.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-5-150x77.jpg 150w\" sizes=\"auto, (max-width: 264px) 100vw, 264px\" \/><\/a>\u00ad<\/p>\n<\/li>\n<li>Ora,<br \/>\n\\[\\begin{array}{*{35}{l}}<br \/>\na(t)=0 &amp; \\Leftrightarrow\u00a0 &amp; -0,5{{t}^{2}}+4t+4,5=0\\wedge t\\ge 0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; t=\\frac{-4\\mp \\sqrt{16+9}}{-1}\\wedge t\\ge 0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; (t=-1\\vee t=9)\\wedge t\\ge 0\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; t=9\u00a0 \\\\<br \/>\n\\end{array}\\]A bola atinge a rua 9 segundos ap\u00f3s o seu lan\u00e7amento, com uma velocidade de -50 m\/s, pois $a'(9)=-9+4=-5$.<\/p>\n<p style=\"text-align: center;\" data-tadv-p=\"keep\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-6.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6571\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6571\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-6.jpg\" data-orig-size=\"264,136\" 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=\"G5\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-6.jpg\" class=\"alignnone size-full wp-image-6571\" title=\"G5\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-6.jpg\" alt=\"\" width=\"211\" height=\"109\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-6.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-6-150x77.jpg 150w\" sizes=\"auto, (max-width: 211px) 100vw, 211px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-7.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6572\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6572\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-7.jpg\" data-orig-size=\"264,136\" 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=\"G6\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-7.jpg\" class=\"alignnone size-full wp-image-6572\" title=\"G6\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-7.jpg\" alt=\"\" width=\"211\" height=\"109\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-7.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-7-150x77.jpg 150w\" sizes=\"auto, (max-width: 211px) 100vw, 211px\" \/><\/a>\u00a0 <a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-8.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6573\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6573\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-8.jpg\" data-orig-size=\"264,136\" 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=\"G7\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-8.jpg\" class=\"alignnone size-full wp-image-6573\" title=\"G7\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-8.jpg\" alt=\"\" width=\"211\" height=\"109\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-8.jpg 264w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/03\/11-pag-194-37-8-150x77.jpg 150w\" sizes=\"auto, (max-width: 211px) 100vw, 211px\" \/><\/a><\/p>\n<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6565' onClick='GTTabs_show(0,6565)'>&lt;&lt; Enunciado<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6565' onClick='GTTabs_show(2,6565)'>Simula\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_6565'>\n<span class='GTTabs_titles'><b>Simula\u00e7\u00e3o<\/b><\/span><\/p>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":719,\r\n\"height\":476,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"showFullscreenButton\":true,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ 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