document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099735>Question 1099735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a system of three equations to solve applied problems\r<BR>\n" );
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document.write( "The concentration of dissolved oxygen in water varies with temperature. Between  0&#8728;C&#8722;50&#8728;C0&#8728;C&#8722;50&#8728;C , the relationship can be modeled as a quadratic function. Use the data in the table below to write a system of equations that, if solved, would help you find the quadratic function.\r<BR>\n" );
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document.write( "T ( &#8728;C)&#8728;C) 	Dissolved oxygen  (mgL)(mgL) <BR>\n" );
document.write( "10	11.27<BR>\n" );
document.write( "20	9.07<BR>\n" );
document.write( "30	7.54 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714189 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=714189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 10	11.27<BR>\n" );
document.write( "20	9.07<BR>\n" );
document.write( "30	7.54<BR>\n" );
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document.write( "since it's a quadratic, find the parabola thru the 3 points.<BR>\n" );
document.write( "y = ax^2 + bx + c<BR>\n" );
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document.write( "11.27 = 100a + 10b + c<BR>\n" );
document.write( "9.07 = 400a + 20b + c<BR>\n" );
document.write( "7.54 = 900a + 30b + c<BR>\n" );
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document.write( "Eliminate c<BR>\n" );
document.write( "9.070 = 400a + 20b + c<BR>\n" );
document.write( "11.27 = 100a + 10b + c<BR>\n" );
document.write( "--------------------------- Subtract<BR>\n" );
document.write( "-2.2 = 300a + 10b  Eqn A<BR>\n" );
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document.write( "7.54 = 900a + 30b + c<BR>\n" );
document.write( "9.07 = 400a + 20b + c<BR>\n" );
document.write( "--------------------------- Subtract<BR>\n" );
document.write( "-1.53 = 500a + 10b  Eqn B<BR>\n" );
document.write( "10b = -1.53 - 500a<BR>\n" );
document.write( "10b = -2.2 - 300a  ---  From Eqn A<BR>\n" );
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document.write( "Since both = 10b:<BR>\n" );
document.write( "-1.53 - 500a = -2.2 - 300a<BR>\n" );
document.write( "200a = 0.67<BR>\n" );
document.write( "a = 0.00335<BR>\n" );
document.write( "Sub for a, find b, then find c<BR>\n" );
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document.write( "There's a \"shortcut\" when the x values are evenly spaced, but this always works.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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