15

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#003333" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> <bR> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> <bR> <bR> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>15</B></div> <div> <B>S u m  a</B></div> <div> <B>Suma de monomios</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <div> <B>P r o c e d i m i e n t o :</B></div> <div> <B>1.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" > Se escriben las expresiones una a continuación de otra y con sus respectivos signos</FONT></div> <div> <B>2.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" > Se reducen los términos semejantes. Para reducir términos semejantes se procede de la siguiente forma:</FONT></div> <div> <B>a.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  Si los términos son de igual signo, se suman los coeficientes y se escribe el signo común</FONT></div> <div> <B>b.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  Si los términos tienen signo distinto, se restan los coeficientes y se escribe el signo del número mayor en valor absoluto</FONT></div> <div> <B>c.</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >  A continuación del signo y del coeficiente se escribe la parte literal</FONT></div> <bR> <div> <I>Nota</I><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" ><I>: recuérdese que los términos semejantes son aquellos sumandos que tienen las mismas letras y afectadas por los </I></FONT></div> <div> <I>mismos exponentes.</I></div> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados de los problemas del Ejercicio 15</B></div> <bR> <div> <B>          S</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >olución en imagen <IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> de los cincuenta problemas del Ejercicio 15:</FONT></div> <div> <B>S</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" > u m a r :</FONT></div> <bR> <div> <IMG SRC="75d140180.gif" border=0 width="64" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#1" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/rZj36NIuGIk" TARGET="_top" TITLE="https://youtu.be/rZj36NIuGIk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75d253180.gif" border=0 width="83" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#2" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/rZj36NIuGIk" TARGET="_top" TITLE="https://youtu.be/rZj36NIuGIk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75d360180.gif" border=0 width="96" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#3" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/rZj36NIuGIk" TARGET="_top" TITLE="https://youtu.be/rZj36NIuGIk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75d460170.gif" border=0 width="96" height="23" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#4" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" 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ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#13" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/rZj36NIuGIk" TARGET="_top" TITLE="https://youtu.be/rZj36NIuGIk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>        <IMG SRC="75de8d180.gif" border=0 width="141" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#14" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/rZj36NIuGIk" TARGET="_top" TITLE="https://youtu.be/rZj36NIuGIk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75df77300.gif" border=0 width="119" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#15" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/KCq7xd8MwXc" TARGET="_top" TITLE="https://youtu.be/KCq7xd8MwXc"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </div> <div> <IMG SRC="75e077300.gif" border=0 width="119" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#16" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/KCq7xd8MwXc" TARGET="_top" TITLE="https://youtu.be/KCq7xd8MwXc"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75e165300.gif" border=0 width="101" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="#17" TITLE="15"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" 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ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75ef99180.gif" border=0 width="153" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/E22JKcn6U4Y" TARGET="_top" TITLE="https://youtu.be/E22JKcn6U4Y"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>        <IMG SRC="75f09f300.gif" border=0 width="159" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/41axHZul_ao" TARGET="_top" TITLE="https://youtu.be/41axHZul_ao"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </div> <div> <IMG SRC="75f1c3300.gif" border=0 width="195" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/41axHZul_ao" TARGET="_top" TITLE="https://youtu.be/41axHZul_ao"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75f2d3190.gif" border=0 width="211" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/DjAsziEBrTs" TARGET="_top" TITLE="https://youtu.be/DjAsziEBrTs"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75f30c190.gif" border=0 width="268" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/DjAsziEBrTs" TARGET="_top" TITLE="https://youtu.be/DjAsziEBrTs"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </div> <div> <IMG SRC="75f4f91b0.gif" border=0 width="249" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/VI7UC3Nhlmk" TARGET="_top" TITLE="https://youtu.be/VI7UC3Nhlmk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75f5fd1b0.gif" border=0 width="253" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/VI7UC3Nhlmk" TARGET="_top" TITLE="https://youtu.be/VI7UC3Nhlmk"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75f645190.gif" border=0 width="325" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/mxEemnxYVhw" TARGET="_top" TITLE="https://youtu.be/mxEemnxYVhw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="75f723190.gif" border=0 width="291" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/J_S22fE3a40" TARGET="_top" TITLE="https://youtu.be/J_S22fE3a40"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75f8ed300.gif" border=0 width="237" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/JZ-pMuSM3C4" TARGET="_top" TITLE="https://youtu.be/JZ-pMuSM3C4"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75f9f8180.gif" border=0 width="248" height="24" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/1YiNtlk9Iww" TARGET="_top" TITLE="https://youtu.be/1YiNtlk9Iww"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75fa7b190.gif" border=0 width="379" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/CtksNkeCCsI" TARGET="_top" TITLE="https://youtu.be/CtksNkeCCsI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75fb21190.gif" border=0 width="289" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/wnYQClSOEkw" TARGET="_top" TITLE="https://youtu.be/wnYQClSOEkw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <IMG SRC="75fc48190.gif" border=0 width="328" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/u3Oc_WZIynI" TARGET="_top" TITLE="https://youtu.be/u3Oc_WZIynI"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="75fd631b0.gif" border=0 width="355" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/Wu1gCnvcAnE" TARGET="_top" TITLE="https://youtu.be/Wu1gCnvcAnE"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="75fef8300.gif" border=0 width="248" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/YqkgdsqnDjY" TARGET="_top" TITLE="https://youtu.be/YqkgdsqnDjY"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="760257300.gif" border=0 width="343" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/Dv9_U-My6Ic" TARGET="_top" TITLE="https://youtu.be/Dv9_U-My6Ic"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       </div> <div> <IMG SRC="760165190.gif" border=0 width="357" height="25" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/TeK3EfJ-nzo" TARGET="_top" TITLE="https://youtu.be/TeK3EfJ-nzo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>       <IMG SRC="760338300.gif" border=0 width="312" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/rz2H6kQons0" TARGET="_top" TITLE="https://youtu.be/rz2H6kQons0"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>      <IMG SRC="760475300.gif" border=0 width="373" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> <A HREF="https://youtu.be/MPqhbffIUTo" TARGET="_top" TITLE="https://youtu.be/MPqhbffIUTo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>¿Qué es una suma de monomios?</B></div> <div> La suma de monomios es una de las operaciones más frecuentes en el álgebra. Un monomio es una expresión algebraica que está formada por un solo término, el cual puede contener variables (letras), coeficientes (números) y exponentes (potencias). Por ejemplo, 2x^3 es un monomio con la variable x, el coeficiente 2 y el exponente 3.</div> <bR> <div> Para sumar dos o más monomios, se deben identificar los términos que son semejantes, es decir, que tienen la misma variable y el mismo exponente. Luego se deben sumar los coeficientes de esos términos y escribir la parte literal (variable y exponente) común. Por ejemplo, para sumar 2x^3 + 5x^3 + 7x^2 + 4x^2 se procede así:}</div> <bR> <DIV ALIGN="LEFT"></DIV> <div> 2x^3 + 5x^3 + 7x^2 + 4x^2 = (2 + 5)x^3 + (7 + 4)x^2 = 7x^3 + 11x^2</div> <bR> <div> En algunos casos, puede haber términos que no tengan ninguna variable específica. Estos términos se llaman constantes y se suman como cualquier otro número. Los términos constantes se escriben al final de la suma de monomios. Por ejemplo, si se quiere sumar 3x + 4y + 5 - x - y - 6 se hace así:</div> <bR> <DIV ALIGN="LEFT"></DIV> <div> 3x + 4y + 5 - x - y -6 = (3 -1)x + (4 -1)y + (5 -6) = 2x + 3y -1</div> <bR> <div> <B>Lista de reproducción sobre las soluciones del Ejercicio 15</B></div> <bR> <div> <B> <iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo2NVtXvjAWpz0_XSvfJrvf0" frameborder="0" allowfullscreen></iframe>  </B></div> <div> <B>S</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" > u m a r :</FONT></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="58df15510.gif" border=0 width="789" height="81" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="592b68510.gif" border=0 width="872" height="81" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="592c34510.gif" border=0 width="820" height="81" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="592d7f500.gif" border=0 width="895" height="80" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="592e616c0.gif" border=0 width="865" height="108" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="592f476c0.gif" border=0 width="839" height="108" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="593035500.gif" border=0 width="821" height="80" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="8"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>8</div> <div> <IMG SRC="58e097510.gif" border=0 width="919" height="81" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="9"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>9</div> <div> <IMG SRC="5931c5510.gif" border=0 width="965" height="81" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="10"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>10</div> <div> <IMG SRC="5932a36c0.gif" border=0 width="931" height="108" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="11"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>11</div> <div> <IMG SRC="5933e4510.gif" border=0 width="996" height="81" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="12"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>12</div> <div> <IMG SRC="5934c46c0.gif" border=0 width="964" height="108" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="13"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>13</div> <div> <IMG SRC="5935db6c0.gif" border=0 width="987" height="108" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="14"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>14</div> <div> <IMG SRC="5936c06c0.gif" border=0 width="960" height="108" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="15"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>15</div> <div> <IMG SRC="58e1a0830.gif" border=0 width="928" height="131" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="16"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>16</div> <div> <IMG SRC="5937997f0.gif" border=0 width="921" height="127" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="17"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>17</div> <div> <IMG SRC="59382db10.gif" border=0 width="813" height="177" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="18"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>18</div> <div> <IMG SRC="5939d8b90.gif" border=0 width="984" height="185" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="19"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>19</div> <div> <IMG SRC="593a0cd70.gif" border=0 width="1036" height="215" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="20"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>20</div> <div> <IMG SRC="593b7cb10.gif" border=0 width="892" height="177" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="21"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>21</div> <div> <IMG SRC="593cc8b90.gif" border=0 width="968" height="185" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <DIV 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