tag:blogger.com,1999:blog-11883218887109011752024-02-07T18:40:44.523-08:00PROBLEMA DE ECUACION CUADRATICABIENVENIDOAnonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-1188321888710901175.post-56424665631070376832012-03-27T17:47:00.005-07:002012-03-27T17:47:36.917-07:00<a href="http://www.youtube.com/watch?v=9veNjGofq7I" target="_blank">como resolver un problema</a>Anonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.com0tag:blogger.com,1999:blog-1188321888710901175.post-17161626805355697732012-03-27T17:47:00.001-07:002012-03-27T17:47:01.682-07:00<a href="http://www.youtube.com/watch?v=TbB-qfWwV3E" target="_blank">formula de la velocidad</a>Anonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.com0tag:blogger.com,1999:blog-1188321888710901175.post-60372788413115354242012-03-27T17:42:00.001-07:002012-03-27T17:42:04.864-07:00<br />
<div class="MsoListParagraph" style="line-height: normal; margin: 0cm 0cm 0pt 36pt; mso-add-space: auto; mso-layout-grid-align: none; mso-list: l0 level1 lfo1; punctuation-wrap: simple; text-align: justify; text-indent: -18pt;">
<span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: Symbol; mso-fareast-language: ES-CO;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
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<span style="font-family: "Arial","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">DOS EMBARCACIONES A Y B PARTEN DEL MISMO PUNTO Y A
LA MISMA HORA EN DIRECCIONES PERPENDICULARES.<o:p></o:p></span></div>
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<div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0pt; mso-layout-grid-align: none; punctuation-wrap: simple; text-align: justify;">
<span style="font-family: "Arial","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">B SE DESPLAZA 7KM/H MAS LENTO QUE A.DESPUES DE 4
HORAS SE <span style="mso-spacerun: yes;"> </span>ENCUENTRAN A UNA
DISTANCIA DE 68 KM/H ENTRE SI. CALCULA LA VELOCIDAD DE LA EMBARCACION.<o:p></o:p></span></div>
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<span style="font-family: "Arial","sans-serif"; mso-bidi-font-family: "Times New Roman"; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: ES-CO;">DESARROLLO DEL PROBLEMA</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhL8mlB-3rjIfY3803OEGyZSnd4l4z951yyLB4wKFay_YO1N0aJC7KWsOkJbG3DCwwjxrFe9EShS_k0V7Su3TULlm98Ngirm600_WbGhIk2v5iaU83wjES4BtARCULhaHMiy3ISNIanliFF/s1600/vvvvvv.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhL8mlB-3rjIfY3803OEGyZSnd4l4z951yyLB4wKFay_YO1N0aJC7KWsOkJbG3DCwwjxrFe9EShS_k0V7Su3TULlm98Ngirm600_WbGhIk2v5iaU83wjES4BtARCULhaHMiy3ISNIanliFF/s640/vvvvvv.png" width="542" /></a></div>Anonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.com0tag:blogger.com,1999:blog-1188321888710901175.post-64981861648193409382012-03-27T12:46:00.001-07:002012-03-27T12:46:03.936-07:00<a href="http://www.youtube.com/watch?v=FTAyKcvWFnY" target="_blank">ESTE ES UN VIDEITO QUE TE VA A AYUDAR MUCHO</a>Anonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.com0tag:blogger.com,1999:blog-1188321888710901175.post-48878662439700599002012-03-25T10:49:00.001-07:002012-03-25T10:49:07.088-07:00<b><span style="color: #777777; font-size: medium;"><span style="color: #777777; font-size: medium;"><span style="color: black; font-family: Arial, Helvetica, sans-serif; font-size: medium;"><div align="LEFT">
Resolución de Problema</div>
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<span style="font-size: x-small;"><span style="color: black; font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Las ecuaciones de primer y segundo grado aparecen</span></span></div>
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<span style="color: black; font-family: Arial, Helvetica, sans-serif;">en multitud de ocasiones en la resolución de distintos</span></div>
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<span style="color: black; font-family: Arial, Helvetica, sans-serif;">problemas de la vida real</span><br />
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<span style="color: black; font-family: Arial, Helvetica, sans-serif; font-size: small;"><strong>Recuerda los pasos:</strong></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"></span></span></span></span><span lang="JA" style="color: #ff6500; font-size: small;"></span><div align="LEFT">
<strong><span style="font-family: Arial, Helvetica, sans-serif;">Comprender el enunciado<span lang="JA" style="color: #ff6500;"></span></span></strong></div>
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<strong><span style="font-family: Arial, Helvetica, sans-serif;">Identificar la incógnita<span lang="JA" style="color: #ff6500;"></span></span></strong></div>
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<strong><span style="font-family: Arial, Helvetica, sans-serif;">Traducir a lenguaje algebraico<span lang="JA" style="color: #ff6500;"></span></span></strong></div>
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<strong></strong></div>
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<strong><span style="font-family: Arial, Helvetica, sans-serif;">Plantear la ecuación<span lang="JA" style="color: #ff6500;"><span lang="JA" style="color: #ff6500;"></span></span></span></strong></div>
<span lang="JA" style="color: #ff6500;"><span lang="JA" style="color: #ff6500;"></span><div align="LEFT">
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<strong><span style="font-family: Arial, Helvetica, sans-serif;">Resolver<span lang="JA" style="color: #ff6500;"></span></span></strong></div>
<span lang="JA" style="color: #ff6500; font-family: Arial, Helvetica, sans-serif;"><strong></strong></span><strong><span style="font-family: Arial, Helvetica, sans-serif;">Comprobar las soluciones</span></strong><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcQN-Fl0dKfX0OhJ9axqYTQcO4piOjtb0k4i66myTRK8e5XyVW2RTZRkfA2p-vA6w0QHEcSxVJI7SldUMQU01WAD4Xiwg6GYqD9uV0VmOouCMJvb0e_SIJ8gJFi69Xk4pqYpmgDnMOv_aP/s1600/Sin+t%C3%ADtulo.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="287" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcQN-Fl0dKfX0OhJ9axqYTQcO4piOjtb0k4i66myTRK8e5XyVW2RTZRkfA2p-vA6w0QHEcSxVJI7SldUMQU01WAD4Xiwg6GYqD9uV0VmOouCMJvb0e_SIJ8gJFi69Xk4pqYpmgDnMOv_aP/s400/Sin+t%C3%ADtulo.jpg" width="400" /></a></div>
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</span></span>Anonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.com0tag:blogger.com,1999:blog-1188321888710901175.post-27469559928943160522012-03-25T10:39:00.004-07:002012-03-25T10:39:58.619-07:00<span style="font-family: Arial; font-size: x-large;">Ecuaciones Cuadráticas </span><br />
<br />
<span style="font-family: Arial; font-size: medium;">Una ecuación cuadrática es una ecuación en su forma ax</span><span style="font-size: small;"><span style="font-family: Arial;"><sup>2 </sup><span style="font-size: medium;">+ bx + c,
donde a, b, y c son números reales.</span></span> </span><br />
<span style="font-size: small;"><span style="font-family: Arial,Helvetica;"><span>Ejemplo:</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>9x<sup>2</sup> + 6x + 10 a =
9, b = 6, c = 10</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>3x<sup>2</sup> - 9x
a = 3, b = -9, c = 0</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>-6x<sup> 2</sup> + 10 a
= -6, b = 0, c = 10</span></span> <br />
<br />
<span style="font-family: Arial,Helvetica;"><span>Hay tres formas de hallar las raíces
( el o los valores de la variable) de las ecuaciones cuadráticas:</span></span>
<br />
<br />
<span style="font-family: Arial,Helvetica;"><span>1. Factorización
Simple</span></span> <br /><span style="font-family: Arial,Helvetica;"><span>2. Completando
el Cuadrado</span></span> <br /><span style="font-family: Arial,Helvetica;"><span>3.
Fórmula Cuadrática</span></span> <br />
<br />
<u><span style="font-family: Arial,Helvetica;"><span>Factorización
Simple:</span></span></u>
<br />
<br />
<span style="font-family: Arial,Helvetica;"><span>La factorización simple consiste en
convertir la ecuación cuadrática en un producto de binomios. Luego, se busca el
valor de x de cada binomio.</span></span><br />
<br />
<span style="font-family: Arial,Helvetica;"><span>Ejemplo: Realizar la factorización
simple de la ecuación</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span> x2 + 2x – 8 = 0 a = 1
b = 2 c = - 8</span></span> <br />
<br />
<span style="font-family: Arial,Helvetica;"><span>(x ) (x ) =
0 [x ·x = x<sup>2</sup>]</span></span> <br />
<br />
<table cols="2">
<tbody>
<tr>
<td><span style="font-family: Arial,Helvetica;"><span>( x + ) (x - ) =
0</span></span></td>
<td><img height="120" src="http://ponce.inter.edu/cremc/exp2.JPG" width="300" /></td></tr>
</tbody></table>
<br />
<br />
<br />
<span><span style="font-family: Arial,Helvetica;">(x + 4 ) (x – 2) =
0 4 </span><i><span style="font-family: Bell MT;">y
</span></i><span style="font-family: Arial,Helvetica;">–2 4 + -2 = 2</span></span>
<br />
<img height="46" src="http://ponce.inter.edu/cremc/image2TB.JPG" width="35" /><span style="font-family: Arial,Helvetica;"><span> 4 ·
-2 = -8</span></span> <br /> <br /> <br /> <br />
<br />
<span style="font-family: Arial,Helvetica;"><span>x + 4 = 0 x – 2 =
0</span></span> <br /> <br /> <br />
<br />
<span style="font-family: Arial,Helvetica;"><span>x + 4 = 0 x – 2 =
0</span></span> <br /><span style="font-family: Arial,Helvetica;"><span>x = 0 – 4 x =
0 + 2</span></span> <br /><span style="font-family: Arial,Helvetica;"><span>x =
-4 x = 2 Estas son las dos soluciones.</span></span>
<br /> <br />
<br />
<u><span style="font-family: Arial,Helvetica;"><span>Completando el
Cuadrado:</span></span></u>
<br />
<span style="font-family: Arial,Helvetica;"><span> En este método, la ecuación tiene
que estar en su forma ax2+bx+c; y siempre la constante de a tiene que ser igual
a 1.</span></span> <br /><span style="font-family: Arial,Helvetica;"><span> Por ejemplo,
para factorizar la ecuación 4x2 + 12x – 8 = 0, hay que despejar de la siguiente
forma:</span></span> <br /> <br />
<br />
<table cols="2">
<tbody>
<tr>
<td><br /><span style="font-family: Arial,Helvetica;"><span><u>4x</u><sup>2</sup> +
<u>12</u>x – <u>8</u> = <u>0</u></span></span> <br /><span style="font-family: Arial,Helvetica;"><span> 4 4 4 4</span></span></td>
<td><img height="40" src="http://ponce.inter.edu/cremc/imageKNN.JPG" width="223" /></td></tr>
</tbody></table>
<br />
<br />
<span style="font-family: Arial,Helvetica;"><span>x<sup>2</sup> + 3x – 2 = 0 Ahora,
a= 1.</span></span> <br />
<br />
<span style="font-family: Arial,Helvetica;"><span>Ejemplo:</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>x<sup>2</sup> + 2x – 8 = 0
[Ya está en su forma donde a = 1.]</span></span> <br /><span style="font-family: Arial,Helvetica;"><span>x<sup>2</sup> + 2x = 8 [
Pasar a c al lado opuesto.]</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>x<sup>2</sup> + 2x + ___ = 8 + ___
[Colocar los blancos]</span></span> <br /> <br /> <br />
<br />
<table cols="2">
<tbody>
<tr>
<td><span style="font-family: Arial,Helvetica;"><span>x<sup>2</sup> + 2x + 1 = 8 +
1</span></span></td>
<td><img height="74" src="http://ponce.inter.edu/cremc/exp3.JPG" width="256" /></td></tr>
</tbody></table>
<br />
<span style="font-family: Arial,Helvetica;"><span>x<sup>2</sup> + 2x + 1 =
9</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>( ) ( ) = 9 Hay
que factorizar.</span></span> <br /><span style="font-family: Arial,Helvetica;"><span> Nota: Siempre será un cuadrado
perfecto.</span></span> <br /> <br /> <br />
<br />
<table cols="2">
<tbody>
<tr>
<td><span style="font-family: Arial,Helvetica;"><span>( x + 1) (x + 1) = 9</span></span>
<span style="font-family: Arial,Helvetica;"><span>(x + 1)<sup>2</sup> =
9</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>(x + 1) = ± </span></span><img height="26" src="http://ponce.inter.edu/cremc/imageDGM.JPG" width="28" />
<br />
</td>
<td><img height="168" src="http://ponce.inter.edu/cremc/exp4.JPG" width="300" /></td></tr>
</tbody></table>
<br />
<br />
<span style="font-family: Arial,Helvetica;"><span>x + 1 = ± 3</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>x = -1 ± 3 [Separar las dos
soluciones.]</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>x = -1 + 3 x = -1 –
3</span></span> <br /><span style="font-family: Arial,Helvetica;"><span>x = 2
x = -4</span></span> <br /> <br /> <br />
<br />
<u><span style="font-family: Arial,Helvetica;"><span>Fórmula
Cuadrática:</span></span></u>
<br />
<span style="font-family: Arial,Helvetica;"><span> Este método es muy simple: hay que
sustituir los valores de a, b y c de la ecuación cuadrática a la siguiente
fórmula:</span></span> <br /> <br /> <br /><br />
<br />
<center>
<img height="54" src="http://ponce.inter.edu/cremc/formula.JPG" width="129" /></center>
<br />
<br /><br /><br /><br />
<br />
<span style="font-family: Arial,Helvetica;"><span>Ejemplo:</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>X<sup>2</sup> + 2x – 8 = 0 a =
1, b = 2, c = -8</span></span> <br /> <br /> <br /> <br />
<br />
<span style="background-color: white;"><img height="429" src="http://ponce.inter.edu/cremc/proceso.JPG" width="249" /></span> <br /><img height="87" src="http://ponce.inter.edu/cremc/proceso2.JPG" width="160" /> <br /> <br />
<br />
<span style="font-family: Arial,Helvetica;"><span>x = <u>-2 ± 6</u></span></span>
<br /><span style="font-family: Arial,Helvetica;"><span> 2</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>X = <u>-2 + 6</u> x = <u>-2 -
6</u></span></span> <br /><span style="font-family: Arial,Helvetica;"><span>
2 2</span></span> <br />
<br />
<span style="font-family: Arial,Helvetica;"><span> x =<u> 4</u> x =
<u>-8</u></span></span> <br /><span style="font-family: Arial,Helvetica;"><span>
2 2</span></span>
<br />
<span style="font-family: Arial,Helvetica;"><span>x = 2 x = - 4</span></span>
<br />
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<br /><br /> <br /> </span>Anonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.com0tag:blogger.com,1999:blog-1188321888710901175.post-86628120924591835652012-03-25T10:29:00.000-07:002012-03-25T10:29:14.132-07:00<h2>
<u><span style="color: black;">BIENVENIDO</span></u></h2>
<br />
A CONTINUACION PODRAS SABER MAS ACERCA DE QUE ES UNA ECUACION CUADRATICA Y DE COMO PROCEDER A RESOLVERLASAnonymoushttp://www.blogger.com/profile/00198084569868369725noreply@blogger.com0