tag:blogger.com,1999:blog-90304421238591032024-02-19T00:43:46.291-08:00MatPrazerO prazer da matemática. Espaço dedicado aos conteúdos do ensino básico e à resolução de problemas.Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.comBlogger41125tag:blogger.com,1999:blog-9030442123859103.post-69668343493123899732011-12-11T05:56:00.001-08:002011-12-11T06:28:36.940-08:00Isometrias - A calçada portuguesa<div dir="ltr" style="text-align: left;" trbidi="on">
</div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-71989344332831146242011-09-11T08:48:00.000-07:002011-09-11T08:51:49.399-07:00A escada<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkufMcPhZ8AsB7MblwN0fYlcQDWiMRElTM9Cb0jcRMhlEpBXPfGmWgwPBzNSdUsz99dvE6fglYQMnhgT6GmXW8i4_0OR7AUrTDkra1m7ycaNtpdQPNuZABRU4-YfsCD6_TO57oH9wzhQ/s1600/escada2.bmp" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="190px" nba="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkufMcPhZ8AsB7MblwN0fYlcQDWiMRElTM9Cb0jcRMhlEpBXPfGmWgwPBzNSdUsz99dvE6fglYQMnhgT6GmXW8i4_0OR7AUrTDkra1m7ycaNtpdQPNuZABRU4-YfsCD6_TO57oH9wzhQ/s200/escada2.bmp" width="200px" /></a></div>
<span class="messageBody" data-ft="{"type":3}" style="color: orange;"><strong>Uma pessoa encontra-se no degrau do meio de uma escada. Sobe <span style="color: #45818e;">5 degraus</span>, <span style="color: #45818e;">desce 7,</span> volta a <span style="color: #45818e;">subir 4</span> e depois <span style="color: #45818e;">mais 9</span> para chegar ao último. Quantos degraus tem a escada?</strong></span></div>
Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-61189658687231873872011-06-05T00:43:00.000-07:002011-06-05T00:43:57.613-07:00A população das cidades<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5ystMNN4FYhZxDQTzzNKnkQQUSKtBEXZuCSLUQUpFRQkMqfMS-ieygAwyuxJIMX_4Nv4blGEiqlhpxLC0pvBF3bUTUALfcyyp0DNOQ180llmzXBV2vFQTuUc0os8J51eyU4cXsHq4jQ/s1600/cidade1.jpg" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="168px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5ystMNN4FYhZxDQTzzNKnkQQUSKtBEXZuCSLUQUpFRQkMqfMS-ieygAwyuxJIMX_4Nv4blGEiqlhpxLC0pvBF3bUTUALfcyyp0DNOQ180llmzXBV2vFQTuUc0os8J51eyU4cXsHq4jQ/s200/cidade1.jpg" t8="true" width="200px" /></a></div><strong><span style="color: #93c47d;">A população da cidade A é o <span style="color: yellow;">triplo </span>da população da cidade B. Supondo que o total das populações das duas cidades é de <span style="color: yellow;">240000 </span>habitantes, qual a população da cidade A?</span></strong></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-88255752734940346052011-06-05T00:39:00.000-07:002011-06-05T00:41:00.348-07:00Qual é o número?<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxmfxJayp4-BrlkYbljsFNapzuo9JoCRdhB3WOMiNOBmQ0RU4bzTuBxcDV5fTUi97PWAAAAfuoESSE3aAZw5lQK2iBW1nME2f0LkHJKTkthS_oTG2tmm7EuMR7shSCGGPkIS_BvHjZIA/s1600/numero20.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="77px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxmfxJayp4-BrlkYbljsFNapzuo9JoCRdhB3WOMiNOBmQ0RU4bzTuBxcDV5fTUi97PWAAAAfuoESSE3aAZw5lQK2iBW1nME2f0LkHJKTkthS_oTG2tmm7EuMR7shSCGGPkIS_BvHjZIA/s200/numero20.jpg" t8="true" width="200px" /></a></div><strong><span style="color: #e69138;">A soma do <span style="color: #d5a6bd;">dobro </span>de um número aumentado de <span style="color: #d5a6bd;">50 unidades</span> é igual ao <span style="color: #d5a6bd;">sêxtuplo</span> desse número diminuído de <span style="color: #d5a6bd;">10 unidades</span>. Qual é o número?</span></strong></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-6228151802334802582011-05-28T07:15:00.000-07:002011-05-28T07:15:23.838-07:00A idade das amigas<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZw5zFX9R62SbDQ_NF6JW2-fZ9qiezCG7ivfygHvQ083_dhSRRupAC1fKM24f5oNyceMjhzpV7fCK1vEPDE1Qr7oqVdm8JZITFGe2mkttqwtYtCOIeyCTTRPlbvPQTLFZd6mX84UzOxg/s1600/amigos4.jpg" imageanchor="1" style="clear: right; cssfloat: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="183px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZw5zFX9R62SbDQ_NF6JW2-fZ9qiezCG7ivfygHvQ083_dhSRRupAC1fKM24f5oNyceMjhzpV7fCK1vEPDE1Qr7oqVdm8JZITFGe2mkttqwtYtCOIeyCTTRPlbvPQTLFZd6mX84UzOxg/s200/amigos4.jpg" t8="true" width="200px" /></a></div><span style="color: #8e7cc3;"><strong>A Inês e a amiga têm no total</strong> <strong><span style="color: #6aa84f;">25 anos</span></strong> <strong>mas a Inês é mais velha <span style="color: #6aa84f;">3 anos.</span> Qual é idade de cada uma delas?</strong> </span></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-80244608730331842162011-05-28T07:12:00.000-07:002011-05-28T07:12:02.253-07:00Linguagem Matemática<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGDPVUguQbwoMQcSeO47ma88T3fbOV3vrgwjuPB2GoPCdcyZPY2Ee7VTvls7E63s77_3y-vG5Pos_ES0TJyt78X0hbJK4vqHVqxtYVNsNEVzOO4kp0d2mnK86M12oOr97z1MipuWqSqA/s1600/linguagem1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGDPVUguQbwoMQcSeO47ma88T3fbOV3vrgwjuPB2GoPCdcyZPY2Ee7VTvls7E63s77_3y-vG5Pos_ES0TJyt78X0hbJK4vqHVqxtYVNsNEVzOO4kp0d2mnK86M12oOr97z1MipuWqSqA/s1600/linguagem1.bmp" t8="true" /></a></div><div class="mall_post_body_text"><strong><span style="color: #bf9000;"></span></strong> </div><div class="mall_post_body_text"><strong><span style="color: #bf9000;">Colocar em linguagem matemática:<br />
a) O quádruplo da soma do dobro de um número com a sua metade.</span></strong></div><div class="mall_post_body_text"><strong><span style="color: #bf9000;">b) A metade do quíntuplo da diferença entre o triplo de um número e oito.</span></strong></div><div class="mall_post_body_text"><strong><span style="color: #bf9000;">c) A diferença entre o cubo de um número e a sua terça parte.</span></strong></div><div class="mall_post_body_text"><strong><span style="color: #bf9000;">d) a soma da quarta parte de um número com o triplo da soma dessa número com a unidade.</span></strong></div></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-20311021248561458142011-05-28T06:50:00.000-07:002011-05-28T07:04:29.712-07:00Escolha Múltipla - equações<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_-a9VxmyGVECrIC8j7HUForFu5ojc4bRku6y4GLGTGo9SBqOeH9-Skcy0yHp_a6NPpjRFDgu73l6Bag1PY9Os1oAIReYexKsyTLK7E63foIS_bsxIkJOvUunv3OUbkB2JFg9OU6WFhg/s1600/escolha.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_-a9VxmyGVECrIC8j7HUForFu5ojc4bRku6y4GLGTGo9SBqOeH9-Skcy0yHp_a6NPpjRFDgu73l6Bag1PY9Os1oAIReYexKsyTLK7E63foIS_bsxIkJOvUunv3OUbkB2JFg9OU6WFhg/s200/escolha.jpg" t8="true" width="197px" /></a></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"><br />
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<strong><span style="color: magenta;"><span style="color: #e06666;">1. Qual é a solução da equação 2x -1 = 2(x - 3) ?</span> </span></strong><br />
<strong><span style="color: magenta;"> <span style="background-color: yellow; color: #990000;">(A)</span> <span style="color: #e06666;">0</span> </span></strong><br />
<strong><span style="color: magenta;"> <span style="background-color: yellow; color: #990000;">(B)</span> <span style="color: #e06666;">-5</span> </span></strong><br />
<strong><span style="color: magenta;"> <span style="background-color: yellow; color: #990000;">(C)</span> <span style="color: #e06666;">conjunto vazio</span> </span></strong><br />
<span style="color: magenta;"><strong> <span style="background-color: yellow; color: #990000;">(D)</span></strong> </span><span style="color: #e06666;"><strong>4</strong></span><br />
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<div class="mall_post_body_text"><span style="color: #e06666;"><strong>2. O triplo da soma de um número com onze.Em linguagem matemática será:</strong></span><br />
<span style="color: magenta;"> <span style="background-color: yellow; color: #990000;"><strong>(A)</strong></span> </span><span style="color: #e06666;"><strong>3x + 11</strong></span><br />
<span style="color: magenta;"> <span style="background-color: yellow; color: #990000;"><strong>(B)</strong></span> </span><span style="color: #e06666;"><strong>(x + 11)/3</strong></span><br />
<span style="color: magenta;"> <span style="color: #990000;"> <strong><span style="background-color: yellow;">(C)</span></strong></span> </span><span style="color: #e06666;"><strong>3(x + 11)</strong></span><br />
<span style="color: magenta;"> <strong><span style="background-color: yellow; color: #990000;">(D)</span></strong> </span><span style="color: #e06666;"><strong>x^3 + 11</strong></span><br />
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</div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"><span style="color: #e06666;"><strong>3. A solução da equação 4 (-x -6) - (-2x) = 3 + x é:</strong></span></div><div class="mall_post_body_text"><span style="color: magenta;"> <span style="background-color: yellow; color: #990000;"><strong>(A)</strong></span> </span><span style="color: #e06666;"><strong>9</strong></span></div><div class="mall_post_body_text"><span style="color: magenta;"> <span style="background-color: yellow; color: #990000;"><strong>(B)</strong></span> </span><span style="color: #e06666;"><strong>conjunto vazio</strong></span></div><div class="mall_post_body_text"><span style="color: magenta;"> <span style="background-color: yellow; color: #990000;"><strong>(C)</strong></span> </span><span style="color: #e06666;"><strong>-9</strong></span></div><div class="mall_post_body_text"><span style="color: magenta;"> <span style="background-color: yellow; color: #990000;"><strong>(D)</strong></span> </span><span style="color: #e06666;"><strong>-27</strong></span></div></div><div class="mall_post_body_text"></div><div class="mall_post_body_text"></div></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-43008983652541638272011-05-28T06:39:00.000-07:002011-05-28T06:39:24.024-07:00Resolvendo equações...passo a passo<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dx9wtHmJJEuYX7mJ93bw_thw5REsHsprIhm6g8ggzv5AmHdGyObzKXmIR1Ht3QjIR0fQSN6K4J_dmpt1WI0' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-27523777604836961352011-05-22T08:20:00.000-07:002011-05-22T08:20:59.070-07:00Os três amigos<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEU0M6A9cRQlzt5_0lXWK5zJ6G31r_GZTY_IyooL3HvPn7pOWVwxZg-5sTOryiqHjtV9sC95rTz7TJ-G8zUEvooO9U4EY7swCd3a-lvsC314JItyMJ0ToCP9pAuvB5XRQjbnZuHIkrJw/s1600/amigos+3.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="193px" j8="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEU0M6A9cRQlzt5_0lXWK5zJ6G31r_GZTY_IyooL3HvPn7pOWVwxZg-5sTOryiqHjtV9sC95rTz7TJ-G8zUEvooO9U4EY7swCd3a-lvsC314JItyMJ0ToCP9pAuvB5XRQjbnZuHIkrJw/s200/amigos+3.jpg" width="200px" /></a></div><strong><span style="color: #6aa84f;">As idades actuais dos amigos Zé, Manel e Tó João correspondem a três números inteiros consecutivos. Sabendo que a soma das suas idades é igual a <span style="color: #cc0000;">51 anos</span> e que o Manel é o mais velho e o Zé o mais novo, qual é a idade do Tó João? E a idade dos outros dois?</span></strong></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-23957745099424791872011-05-22T08:16:00.000-07:002011-05-22T08:16:51.718-07:00A idade das amigas<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja_eBZsl6pgRKVEVCEy5IoLZkRMErg21j1hLgEqqkPNdz75rs_La3OkCmlbwuhHAOb_K6fMniQw3GYTRROuSv8K1flI1T9QCFfj1CDkeXR7q1T8qV0XOxRh7I5S9OBuEWyB1ppJHPcHQ/s1600/amigas1.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200px" j8="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja_eBZsl6pgRKVEVCEy5IoLZkRMErg21j1hLgEqqkPNdz75rs_La3OkCmlbwuhHAOb_K6fMniQw3GYTRROuSv8K1flI1T9QCFfj1CDkeXR7q1T8qV0XOxRh7I5S9OBuEWyB1ppJHPcHQ/s200/amigas1.jpg" width="185px" /></a></div><strong><span style="color: orange;">A Joana e a Rita, amigas de longa data, fazem uma diferença de <span style="color: #e06666;">4 anos</span> sendo a Rita a mais velha.A soma das suas idades actuais é de <span style="color: #e06666;">38 anos</span>. </span></strong><br />
<strong><span style="color: orange;">Que idade terá cada uma delas daqui a <span style="color: #e06666;">3 anos</span>?</span></strong><br />
<div class="UIImageBlock_Content UIImageBlock_MED_Content fsm fwn fcg"><div class="uiAttachmentDesc"></div></div></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-55660863251622601882011-05-08T09:19:00.000-07:002011-05-08T09:34:54.217-07:00Procedimento para a resolução de equações do primeiro grau com uma incógnita<div dir="ltr" style="text-align: left;" trbidi="on"><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6pfgp1hZPFVD96OpgtQsxjHXMDYVQAPofj1fEE7XQh_dMloIz38J0i5JlptyDIsOnzFjGLViJ6tI6nIfnCNLvPmqmLZtcTGpsodOEQ6uOqAHaXRDsiDf7pzcjlHjODramRsc_4S7C4g/s1600/equa%25C3%25A7oes1.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="152px" j8="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6pfgp1hZPFVD96OpgtQsxjHXMDYVQAPofj1fEE7XQh_dMloIz38J0i5JlptyDIsOnzFjGLViJ6tI6nIfnCNLvPmqmLZtcTGpsodOEQ6uOqAHaXRDsiDf7pzcjlHjODramRsc_4S7C4g/s400/equa%25C3%25A7oes1.jpg" width="400px" /></a><span style="font-family: Arial;"></span><span style="font-family: Arial;"><span style="background-color: white; color: #93c47d;"><strong></strong></span></span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><br />
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</div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><ul style="text-align: left;"><li><span style="font-family: Arial;"><span style="background-color: white; color: #93c47d;"><strong>Tirar parênteses (aplicando as regras com muita atenção).</strong></span></span><span style="font-family: Arial;"><span style="background-color: white;"> </span></span></li>
<li><span style="font-family: Arial;"><span style="color: #f1c232;"><span style="background-color: white;"><strong>Desembaraçar de denominadores</strong>.</span></span></span><span style="font-family: Arial;"> </span></li>
<li><span style="font-family: Arial;"><span style="background-color: white; color: #8e7cc3;"><strong>Passar para um dos membros os termos com a incógnita e para o outro membro os termos independentes.</strong></span></span><span style="font-family: Arial;"> </span></li>
<li><span style="font-family: Arial;"><strong><span style="background-color: white; color: #6fa8dc;">Simplificar cada membro.</span></strong></span><span style="font-family: Arial;"><span style="background-color: #f3f3f3;"> </span></span></li>
<li><span style="font-family: Arial;"><span style="background-color: white; color: #cc0000;"><strong>Obter o valor da incógnita.</strong></span></span><span style="font-family: Arial;"> </span></li>
<li><span style="font-family: Arial;"><strong><span style="background-color: white; color: #b45f06;">Indicar o conjunto solução.</span></strong></span></li>
<li><span style="font-family: Arial;"><strong><span style="background-color: white; color: magenta;">Verificar a solução encontrada.</span></strong><br />
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<span style="color: blue; font-family: TimesNewRoman; font-size: medium;"><span style="color: blue; font-family: TimesNewRoman; font-size: medium;"><span style="color: blue; font-family: TimesNewRoman; font-size: medium;"><span style="color: #b6d7a8;"><strong><u>Exemplos:</u></strong></span></span></span></span></span></li>
</ul></div><span style="background-color: #ffe599;"><span style="font-family: Arial;"><span style="font-family: TimesNewRoman; font-size: medium;"><span style="font-family: TimesNewRoman; font-size: medium;"><span style="color: black; font-family: TimesNewRoman; font-size: medium;">Resolve as equações:</span></span></span></span></span><span style="background-color: #ffe599;"><br />
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<ul><li><span style="background-color: #ffe599; color: black;">x + 7 = 10 - 2</span></li>
<li><span style="background-color: #ffe599; color: black;">2x + 3 = 17</span></li>
<li><span style="background-color: #ffe599; color: black;">6 - (x - 5) = 4 + (3 - 5x)</span></li>
<li><span style="background-color: #ffe599; color: black;">-2 (x - 2) = 5 - (1 - x)</span></li>
</ul></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-69419714350275509122011-04-23T12:13:00.000-07:002011-04-23T12:13:20.465-07:00Números primos<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzC8ZqU-qRprC9CRW_P85SrebBdkX54R8NU-Wa9QveXBU12pKi-6sSaCWYivg8Oi6cL1vMGmX_j9fJMh2d-' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-83416122177292837862011-04-21T03:50:00.000-07:002011-04-21T03:51:38.980-07:00A soma de inteiros de 1 até 1000<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYYITCOi_JZogdaNIrvuCuBcITj2cYMpdgp3WCv-IaKUvARJ25QP0En8kN-0NrKv_EG1LqVg1vr3a5Yj6NgcT8xxvpyXjR7vy4zYIYxMTosYmU32kQcLGPfG2FEvgWcDeDNqfhYymNLA/s1600/soma.bmp" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" i8="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYYITCOi_JZogdaNIrvuCuBcITj2cYMpdgp3WCv-IaKUvARJ25QP0En8kN-0NrKv_EG1LqVg1vr3a5Yj6NgcT8xxvpyXjR7vy4zYIYxMTosYmU32kQcLGPfG2FEvgWcDeDNqfhYymNLA/s1600/soma.bmp" /></a></div><strong><span style="color: #6aa84f;">Sem recorrerres à calculadora, nem a papel e lápis, és capaz de calcular mentalmente e de forma rápida a soma de todos os números inteiros de 1 até 1000?</span></strong></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-3870965713436020792011-02-17T07:08:00.000-08:002011-02-17T07:30:38.143-08:00Enchendo a banheira<div dir="ltr" style="text-align: left;" trbidi="on"><span style="font-family: TTE1BFF728t00; font-size: xx-small;"><span style="font-family: TTE1BFF728t00; font-size: xx-small;"></span></span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRz2xf1xqz3HipkSZKbNdVGvzO6QHswWCI_5TyIy5ZtjdWbVRNsppTwr4adz68hO_cu3k9gYEhuIRolBDm_nezm4ShR6i59wXxZuhW1dbblURm6bZ1l8UKgGypCbdksMFsWecHWS-b5g/s1600/banheira2.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; height: 139px; margin-bottom: 1em; margin-right: 1em; width: 131px;"><img border="0" height="320" j6="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRz2xf1xqz3HipkSZKbNdVGvzO6QHswWCI_5TyIy5ZtjdWbVRNsppTwr4adz68hO_cu3k9gYEhuIRolBDm_nezm4ShR6i59wXxZuhW1dbblURm6bZ1l8UKgGypCbdksMFsWecHWS-b5g/s320/banheira2.jpg" width="289" /></a></div><div align="left"><br />
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<span style="color: #f1c232;"><strong><span style="font-size: small;">Uma torneira lança água durante algum tempo. Os dados registaram-se na seguinte </span><span style="font-size: small;">tabela:</span></strong></span></div><div align="left"><span style="color: #d9d2e9; font-size: small;"><strong>Tempo ( em minutos) 3 4 5 6</strong></span></div><strong><span style="color: #d9d2e9; font-size: small;">Quantidade de água ( em litros) 8,4 11,2 14 16,8</span></strong><br />
<strong><span style="color: #f1c232; font-size: small;">a) Verifique se a quantidade de água é directamente proporcional </span><span style="color: #f1c232;">ao tempo <span style="font-size: small;">e </span><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-size: small;">justifique a sua resposta.</span></span></span> </span></strong><br />
<span style="font-size: small;"><span style="color: #f1c232;"><strong><span style="font-family: TTE1BFF728t00;"><span style="font-family: TTE1BFF728t00;">b) Tendo em conta a resposta dada na alínea anterior, </span></span><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;">indique o <span style="color: #38761d;">valor da constante.</span></span></span></span></strong></span></span><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="color: #f1c232; font-family: TTE1A770C8t00;"> </span></span></span><br />
<span style="font-size: small;"><span style="color: #f1c232;"><strong><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;">c) Qual o significado da constante</span></span></span><span style="font-family: TTE1BFF728t00;"><span style="font-family: TTE1BFF728t00;">, neste problema?</span></span></strong></span></span><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="color: #f1c232; font-family: TTE1A770C8t00;"> </span></span></span><br />
<span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="color: #f1c232; font-size: small;"><strong>d) Complete:</strong></span></span></span></span><br />
<div align="left"><span style="color: #f1c232; font-size: small;"><strong> <span style="color: red;">Quantidade de água = ………..x tempo</span></strong></span><br />
<span style="font-size: small;"><span style="color: red;"><strong><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"> Tempo = ………. x q</span></span><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;">uantidade de água</span></span></strong></span></span><br />
<span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"></span></span></span><strong><span style="color: #f1c232;"><span style="font-size: small;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;">e) Calcule a quantidade de água </span></span></span><span style="font-family: TTE1BFF728t00;"><span style="font-family: TTE1BFF728t00;">que foi lançada ao fim de <span style="color: #e06666;">8</span></span></span><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="color: #e06666;"> minutos</span>. E ao fim de um <span style="color: #e06666;">quarto de hora</span>? </span></span></span></span></strong><br />
<strong><span style="color: #f1c232;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-size: small;">f</span></span></span></span></span><span style="color: #f1c232;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-size: small;">) </span></span></span></span><span style="font-size: small;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;">Determine ao fim de quanto tempo </span></span></span><span style="font-family: TTE1BFF728t00;"><span style="font-family: TTE1BFF728t00;">foi lançada uma quantidade de água de </span></span><span style="font-family: TTE1A770C8t00;"><span style="font-family: TTE1A770C8t00;"><span style="color: #0b5394;">36,4 litros</span>.</span></span></span></span></strong></div><br />
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<div align="left"><strong></strong></div></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-59196340199896268962011-01-30T05:28:00.000-08:002011-01-30T05:39:26.858-08:00Recursos de Matemática para o 7º ano (Lisboa Editora)<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixpGL6s7rIYoWn1pFpTGnV1Fj4ijCKq-6sR-LKZ6uDTnUcHQ52CvEgwsCxk71UcctLQ-jR1V7hFkD5HmUG6X-mHPaSoL9si9CeoHHaJjOB3oBnpcSxZXpKgQheJS2xkB9XMlmlR4AOfg/s1600/lisboa+editora.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="105" s5="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixpGL6s7rIYoWn1pFpTGnV1Fj4ijCKq-6sR-LKZ6uDTnUcHQ52CvEgwsCxk71UcctLQ-jR1V7hFkD5HmUG6X-mHPaSoL9si9CeoHHaJjOB3oBnpcSxZXpKgQheJS2xkB9XMlmlR4AOfg/s200/lisboa+editora.jpg" width="200" /></a></div><br />
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<span style="color: #990000;"><strong>Jogo dos Divisores de um Número</strong></span><br />
<a href="http://www.lisboaeditora.pt/assets/Uploads/2NN7.swf">http://www.lisboaeditora.pt/assets/Uploads/2NN7.swf</a><br />
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<span style="color: #274e13;"><strong>Recta Numérica</strong></span><br />
<a href="http://www.lisboaeditora.pt/assets/Uploads/NR62.swf">http://www.lisboaeditora.pt/assets/Uploads/NR62.swf</a><br />
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<span style="color: yellow;"><strong>Fracções</strong></span><br />
<a href="http://www.lisboaeditora.pt/assets/Uploads/NR61.swf">http://www.lisboaeditora.pt/assets/Uploads/NR61.swf</a><br />
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<strong><span style="color: #c27ba0;">Percentagens</span></strong><br />
<a href="http://www.lisboaeditora.pt/assets/Uploads/NR64.swf">http://www.lisboaeditora.pt/assets/Uploads/NR64.swf</a></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-50934059511674252272011-01-06T09:47:00.000-08:002011-01-06T09:47:57.195-08:00Sabias que...<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivTAzbDTS6GNxqLruF330eK3yTFhbrzGTUxTtXL2HZa2xAynp79dAQmePzq5RTR0g9oQPE5J21I3JCkIGr6uc5NK8x3dGkqKzlFhzXZEZW75pY2eHOMki_ozFP-OucCLlCiDkTbV5JJQ/s1600/sabias2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" n4="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivTAzbDTS6GNxqLruF330eK3yTFhbrzGTUxTtXL2HZa2xAynp79dAQmePzq5RTR0g9oQPE5J21I3JCkIGr6uc5NK8x3dGkqKzlFhzXZEZW75pY2eHOMki_ozFP-OucCLlCiDkTbV5JJQ/s1600/sabias2.jpg" /></a></div><strong><span style="color: #6aa84f;">2011 é um número primo que pode ser expresso como a soma de números primos consecutivos:<br />
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2011 = 157 + 163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211</span></strong><br />
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(<em>Paulo Ferro - professor de Matemática</em>)Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-41949493779612407312011-01-02T08:03:00.000-08:002011-01-02T08:05:59.179-08:00O DIA DOS NAMORADOS<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUATUOR0yF8Z7dOCF-2KgP4Ic8Ia01X0iZJQ0SBtsd2zQ_mbq3s27Yju1hKFIw8vMksOLbiIu-v3IfeSTpyvK33U4fJyfljpJsyixWkQw32OFV4JlMEZ_3-6K6LJp0CqQlYPwHWnzFqA/s1600/namorados4.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" n4="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUATUOR0yF8Z7dOCF-2KgP4Ic8Ia01X0iZJQ0SBtsd2zQ_mbq3s27Yju1hKFIw8vMksOLbiIu-v3IfeSTpyvK33U4fJyfljpJsyixWkQw32OFV4JlMEZ_3-6K6LJp0CqQlYPwHWnzFqA/s200/namorados4.jpg" width="165" /></a></div><br />
<span style="color: #f1c232; font-family: 'Tahoma','sans-serif';"><strong>No dia dos Namorados , cinco amigos e as respectivas namoradas estão num centro comercial. À sua frente, da esquerda para a direita, têm cinco lojas: uma perfumaria, uma loja de CD's, uma livraria, uma loja de bombons e uma florista. </strong></span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="color: #f1c232; font-family: 'Tahoma','sans-serif';"><strong>Os amigos estão a par dos gostos das namoradas e sabem que: </strong></span></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><strong><span style="color: #f1c232;"><span style="font-family: 'Tahoma','sans-serif';">1 -</span><span style="font-family: 'Tahoma','sans-serif';"> A namorada do Filipe quer qualquer coisa excepto bombons.</span></span></strong></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><strong><span style="color: #f1c232;"><span style="font-family: 'Tahoma','sans-serif';">2 -</span><span style="font-family: 'Tahoma','sans-serif';"> A namorada do Luís quer um livro, bombons ou flores. </span></span></strong></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><strong><span style="color: #f1c232;"><span style="font-family: 'Tahoma','sans-serif';">3 - </span><span style="font-family: 'Tahoma','sans-serif';">A namorada do Rui não quer CD's nem bombons. </span></span></strong></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><strong><span style="color: #f1c232;"><span style="font-family: 'Tahoma','sans-serif';">4 - </span><span style="font-family: 'Tahoma','sans-serif';">A namorada do Pedro quer um perfume, bombons ou flores.</span></span></strong></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><strong><span style="color: #f1c232;"><span style="font-family: 'Tahoma','sans-serif';">5 - </span><span style="font-family: 'Tahoma','sans-serif';">A namorada do Tiago não quer livros nem bombons. </span></span></strong></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: 'Tahoma','sans-serif';"></span><span style="color: #f1c232; font-family: 'Tahoma','sans-serif';"><strong>Quando foram comprar prendas, de acordo com o desejo das namoradas, cada um entrou na sua loja. </strong></span></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="color: #f1c232; font-family: 'Tahoma','sans-serif';"><strong>O Luís e o Tiago entraram em lojas uma ao lado da outra. </strong></span></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: 'Tahoma','sans-serif';"></span><span style="color: #f1c232; font-family: 'Tahoma','sans-serif';"><strong>O Pedro e o Filipe entraram em lojas afastadas uma da outra. </strong></span></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: justify;"><span style="font-family: 'Tahoma','sans-serif';"></span><span style="font-family: 'Tahoma','sans-serif';"><span style="color: #f1c232;"><strong>Que prenda recebeu cada uma das namoradas</strong>?</span></span></div><span style="font-family: 'Times New Roman','serif'; font-size: 12pt; mso-ansi-language: PT; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: PT;"> </span>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-55018636103391842042011-01-01T15:38:00.000-08:002011-01-01T15:38:52.810-08:00OS APERTOS DE MÃO<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSef5GXwX4JPHcQj4z5CwoQqqcL2BYtiRgWJRH9V59S3ahapXvSoiRaQrYsM-rqtD-ajcrtxwJUJhFGnS8oHBAW6PLJNADQ1b6DED3bdIAn_KAw585aI-ZTq4WHYyJuCRVZSynqoIEZA/s1600/cavaleiro2.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" n4="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSef5GXwX4JPHcQj4z5CwoQqqcL2BYtiRgWJRH9V59S3ahapXvSoiRaQrYsM-rqtD-ajcrtxwJUJhFGnS8oHBAW6PLJNADQ1b6DED3bdIAn_KAw585aI-ZTq4WHYyJuCRVZSynqoIEZA/s200/cavaleiro2.jpg" width="152" /></a></div><br />
<span style="font-family: 'Tahoma','sans-serif'; mso-ansi-language: PT; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: PT;"><strong><span style="color: #6aa84f;">Catorze cavaleiros foram convidados por El Rei D. Afonso Henriques para uma refeição sumptuosa no castelo de Guimarães. Antes de se sentarem, cada um dos catorze <span style="font-family: 'Tahoma','sans-serif';">cavaleiros apertou a mão a todos os outros. </span></span></strong></span><br />
<span style="font-family: 'Tahoma','sans-serif'; mso-ansi-language: PT; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: PT;"><strong><span style="color: #6aa84f;">Quantos apertos de mão houve?</span></strong></span>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-68260877114082955862011-01-01T15:23:00.000-08:002011-01-01T15:41:03.634-08:00O FAROL<span style="color: #ea9999; font-family: 'Tahoma','sans-serif';"><strong>Numa zona costeira existem 2 faróis para ajudar a navegação. </strong></span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="color: #ea9999; font-family: 'Tahoma','sans-serif';"><strong>Um deles emite um feixe luminoso de <span style="color: #45818e;">18 em 18 segundos</span>, o outro de <span style="color: #38761d;">meio em meio minuto</span>. </strong></span></div><div class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="color: #ea9999; font-family: 'Tahoma','sans-serif';"><strong>Num determinado momento, um barco situado entre os 2 faróis vê simultaneamente os dois feixes luminosos. </strong></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP-GTaH_Jo5m9yMX2cq9ygQwW5N3o5NQAw981nPdBaVF8uHXhpFPKeh3fZWFuJ5YRusEqzxpl75wxrZliBLZ19xEkpZvLMmk_GSJcVrsUFikmwToAiy60kjuQiUVK5V2cBcjQXVh-NwA/s1600/farol1.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><strong><span style="color: #ea9999;"><img border="0" height="200" n4="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP-GTaH_Jo5m9yMX2cq9ygQwW5N3o5NQAw981nPdBaVF8uHXhpFPKeh3fZWFuJ5YRusEqzxpl75wxrZliBLZ19xEkpZvLMmk_GSJcVrsUFikmwToAiy60kjuQiUVK5V2cBcjQXVh-NwA/s200/farol1.jpg" width="197" /></span></strong></a></div><span style="color: #ea9999; font-family: 'Tahoma','sans-serif'; mso-ansi-language: PT; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: PT;"><strong>Passado quanto tempo é que no barco se voltam a ver os dois sinais em simultâneo? </strong></span>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-71510573942440456812010-12-29T04:50:00.000-08:002010-12-29T04:56:37.242-08:00Labirinto dos Múltiplos e Divisores<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiyBp_iODY0BnyptIT__Po90V2hiSDM38Frt7h6hl8BnmRjXq23PRvxGHQKL68uAlV8ogOPvS_Fjtoxbm42XeCyPfdeBIlk9321DB8xRinjIuTnZKT5qhBSHmzYyyXQpIi-m5Axcivag/s1600/Imagem+5485.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" n4="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiyBp_iODY0BnyptIT__Po90V2hiSDM38Frt7h6hl8BnmRjXq23PRvxGHQKL68uAlV8ogOPvS_Fjtoxbm42XeCyPfdeBIlk9321DB8xRinjIuTnZKT5qhBSHmzYyyXQpIi-m5Axcivag/s320/Imagem+5485.jpg" width="320" /></a></div><span style="color: #ffd966;"><strong>A Maria joga com o irmão sempre com a seguinte regra:"só é possível avançar de um número para o seguinte se este for múltiplo ou divisor do anterior. Perde o primeiro que não acertar". Qual o número a partir do qual não é permitido avançar mais?</strong></span><br />
<span style="color: #eeeeee;"><em><strong>(Passatempos de Matemática - Porto Editora)</strong></em></span>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-88933053873548962502010-12-26T13:18:00.000-08:002010-12-29T04:54:22.573-08:00Quadrado mágico com potências<h3 style="margin: 10pt 0cm 0pt;"><span style="font-size: 26pt; line-height: 115%;"></span></h3><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom: medium none; border-collapse: collapse; border-left: medium none; border-right: medium none; border-top: medium none; margin: auto auto auto 62.1pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184;"><tbody>
<tr style="height: 47pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; height: 47pt; mso-border-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.15pt;" valign="top" width="56"><div align="center" class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt; text-align: center;"><span style="font-size: 36pt;"><span style="font-family: Calibri;"><span style="color: #f1c232;">2<sup>6</sup></span></span></span></div></td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; height: 47pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.1pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="color: #f1c232;"><br />
</span></div></td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; height: 47pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.1pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 36pt;"><span style="font-family: Calibri;"><span style="color: #f1c232;">2<sup>8</sup></span></span></span></div></td></tr>
<tr style="height: 50.05pt; mso-yfti-irow: 1;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: #ece9d8; height: 50.05pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.15pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="mso-spacerun: yes;"><span style="color: #f1c232; font-family: Calibri;"> </span></span></div></td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; height: 50.05pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.1pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 36pt;"><span style="font-family: Calibri;"><span style="color: #f1c232;">2<sup>5</sup></span></span></span></div></td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; height: 50.05pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.1pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="color: #f1c232;"><br />
</span></div></td></tr>
<tr style="height: 50.8pt; mso-yfti-irow: 2; mso-yfti-lastrow: yes;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: #ece9d8; height: 50.8pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.15pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="font-size: 36pt;"><span style="font-family: Calibri;"><span style="color: #f1c232;">2<sup>2</sup></span></span></span></div></td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; height: 50.8pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.1pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><br />
</div></td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; height: 50.8pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 42.1pt;" valign="top" width="56"><div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt;"><span style="color: #6fa8dc;"><br />
</span></div></td></tr>
</tbody></table><br />
<div class="MsoNormal" style="margin: 0cm 0cm 10pt;"><br />
</div><div class="MsoNormal" style="margin: 0cm 0cm 10pt; text-align: justify;"><span style="font-size: 14pt; line-height: 115%;"><span style="color: #38761d; font-family: Calibri;"><strong>Complete com potências de base <i style="mso-bidi-font-style: normal;">2</i> de modo a obter um quadrado mágico (o produto das potências em linha, coluna ou diagonal deve ser sempre o mesmo)</strong></span></span><br />
<strong><span style="color: #eeeeee; font-family: Calibri;">(<em>Passatempos de Matemática- Porto Editora</em>)</span></strong></div>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-71338842692930750582010-12-26T12:42:00.001-08:002010-12-29T04:58:02.314-08:00<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhES0ap3BIVCKnBWf7SCWUPIOdT2lFGi8lPd8u9Lum1bmLiaQFjql0cEViCYPLNhntzCXw-26VZyozdP0WqTR4KlAut9MOU52nBSO_nazITWxJGid3Ojx6YSszMG26nhHy9Z9co57WXwQ/s1600/Imagem+5490.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" n4="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhES0ap3BIVCKnBWf7SCWUPIOdT2lFGi8lPd8u9Lum1bmLiaQFjql0cEViCYPLNhntzCXw-26VZyozdP0WqTR4KlAut9MOU52nBSO_nazITWxJGid3Ojx6YSszMG26nhHy9Z9co57WXwQ/s200/Imagem+5490.jpg" width="200" /></a></div><img border="0" height="0" src="http://c.gigcount.com/wildfire/IMP/CXNID=2000002.0NXC/bHQ9MTI5MzM5NjAzODc1MCZwdD*xMjkzMzk2MTQzMjUwJnA9MTgwMzMxJmQ9Jm49YmxvZ2dlciZnPTEmbz*4ZDk4NGUwNDExZDI*/YzEyYmQ3OGIzMDM4ZDFkYjYyNCZvZj*w.gif" style="height: 0px; visibility: hidden; width: 0px;" width="0" /><a href="http://www.scribd.com/word/view/45923194"><strong>ENIGMA DOS SÍMBOLOS</strong></a><br />
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<strong><span style="background-color: #eeeeee;"><em>(Passatempos de Matemática - Porto Editora)</em></span></strong>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-50467612030351775022010-11-01T09:19:00.000-07:002010-12-27T00:51:48.595-08:00O número do Joker<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge5B8l1GIrtoYFHoLNFd2re6EP5hADzUmZHHLnjxyyxpbM0dONMF2xRo3HTqQb_jIR5wZoO4xY77GoerNGRutYr5GJowngimAn8xnFh62KxGAq0OtFMSFOdKYxcLcqAnJE-HrCL1Xa5g/s1600/Imagem+4761.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" nx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge5B8l1GIrtoYFHoLNFd2re6EP5hADzUmZHHLnjxyyxpbM0dONMF2xRo3HTqQb_jIR5wZoO4xY77GoerNGRutYr5GJowngimAn8xnFh62KxGAq0OtFMSFOdKYxcLcqAnJE-HrCL1Xa5g/s200/Imagem+4761.jpg" width="200" /></a></div><strong>Considere o número do Joker (<span style="background-color: #eeeeee; color: #0b5394;">1090704</span>) deste boletim do Euromilhões.</strong><br />
<strong>a) Calcule o <span style="color: red;">m.d.c.</span> e o <span style="color: lime;">m.m.c.</span> entre o número formado pelos terceiro e quarto algarismos e o número formado pelos quinto e sexto algarismos.</strong><br />
<strong>b) Adicione todos os algarismos do número do Joker e indique o conjunto dos seus divisores. Será esse número um <span style="background-color: #f3f3f3; color: #b45f06;">número perfeito</span>? Justifique.</strong><br />
<strong>c) Vá ao encontro dos três últimos algarismos do joker. Decomponha esse número, formado pelos três últimos algarismos, num <span style="color: magenta;">produto de factores primos</span>.</strong>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-71928878636996951252010-11-01T08:48:00.000-07:002010-12-27T09:51:48.089-08:00A gripe do Carlos<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw6x68mqSfnM3oT44dcdh0IYefnOHy8LQs62Ryd3Rlg9hMXyFZ1KWOz-RQ1J0fN0e4yQH10Q3X_fzUkn1wKr9shGNYAeQbuIA-v5Q_mFh7wbyt6jpBZCjLPRa4mrSbcqi4ZRhUb5BjGQ/s1600/doente2.bmp" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="165" nx="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw6x68mqSfnM3oT44dcdh0IYefnOHy8LQs62Ryd3Rlg9hMXyFZ1KWOz-RQ1J0fN0e4yQH10Q3X_fzUkn1wKr9shGNYAeQbuIA-v5Q_mFh7wbyt6jpBZCjLPRa4mrSbcqi4ZRhUb5BjGQ/s200/doente2.bmp" width="200" /></a></div><span style="color: yellow;"><strong>O Carlos encontra-se engripado e por indicação médica tem de tomar dois medicamentos (A e B). O medicamento A deve ser tomado de <span style="background-color: #eeeeee; color: #45818e;">18 em 18 horas</span> e o medicamento B de <span style="background-color: #eeeeee; color: #cc0000;">12 em 12 horas</span>. Sabendo que o Carlos começou a tomar os dois medicamentos às <span style="color: #6aa84f;"><span style="background-color: #eeeeee;">8 horas e 30</span> <span style="background-color: #eeeeee;">minutos</span></span> de um determinado dia, descubra a que horas é que o Carlos voltou a tomar os dois medicamentos em simultâneo.</strong></span>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0tag:blogger.com,1999:blog-9030442123859103.post-82446033235318876652010-09-26T07:14:00.000-07:002010-12-26T15:58:03.723-08:00Bicicletas e triciclos<span style="color: #cc0000;"><strong>No jar</strong></span><a href="http://www.espaciofuturo.com/images/p-i-triciclo-g.jpg"><span style="color: #cc0000;"><strong><img alt="" border="0" height="88" src="http://www.espaciofuturo.com/images/p-i-triciclo-g.jpg" style="cursor: hand; float: left; height: 88px; margin: 0px 10px 10px 0px; width: 95px;" /></strong></span></a><span style="color: #cc0000;"><strong>dim da cidade, no domingo passado, a Joana ficou encantada por encontrar várias bicicletas e triciclos.</strong></span><br />
<span style="color: #cc0000;"><strong>Eram de vários tamanhos e cores, mas ao fazer uma contagem descobriu que havia um total de 12 rodas.</strong></span><br />
<span style="color: #ffcc33; font-size: 130%;"><span style="font-size: large;"><strong></strong></span></span><br />
<blockquote><strong><span style="color: #ffcc33; font-size: 130%;"><span style="font-size: large;">Quantas bicicletas é que a Joana encontrou? E quantos triciclos?</span></span> </strong></blockquote>Daniel Bragahttp://www.blogger.com/profile/13053251413528247207noreply@blogger.com0