document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251715>Question 251715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i find the quadratic equation,with this question:<BR>\n" );
document.write( "\" A rancher wants to yield the max amount of edible beef off of his square mile of land. At first he finds that as he adds more cattle, his yield goes up. However, if he overgrazes, the yield goes down. An agricultural agent tell him that his yield will vary quadratically with the # of animals that he grazes. For 5 head of cattle, his production is 8750 pounds of beef, and for 10 head of cattle, he reaps 15,000 pounds of beef. He had no production when he was grazing no cattle.\"\r<BR>\n" );
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document.write( "Find the particular equation of this function expressing pounds of beef produced in terms of the number of cattle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183492 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183492\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \" A rancher wants to yield the max amount of edible beef off of his square mile of land. At first he finds that as he adds more cattle, his yield goes up.<BR>\n" );
document.write( " However, if he overgrazes, the yield goes down. An agricultural agent tell him that his yield will vary quadratically with the # of animals that he grazes.<BR>\n" );
document.write( " For 5 head of cattle, his production is 8750 pounds of beef, and for 10 head of cattle, he reaps 15,000 pounds of beef.<BR>\n" );
document.write( " He had no production when he was grazing no cattle.\"\r<BR>\n" );
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document.write( "Find the particular equation of this function expressing pounds of beef produced in terms of the number of cattle.<BR>\n" );
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document.write( "Using the form; ax^2 + bx + c = y, c=0, find a and b<BR>\n" );
document.write( "x=5 (no. of cattle); y=8750 (lb of beef)<BR>\n" );
document.write( "a(5^2) + 5b = 8750<BR>\n" );
document.write( "25a + 5b = 8750<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=10; y=15000<BR>\n" );
document.write( "100a + 10b = 15000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st equation by 2, subtract from the above equation<BR>\n" );
document.write( "100a + 10b = 15000<BR>\n" );
document.write( " 50a + 10b = 17500<BR>\n" );
document.write( "---------------------subtraction eliminates b, find a<BR>\n" );
document.write( "50a = -2500<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2500%29%2F50 ALIGN=MIDDLE  ALT=\"%28-2500%29%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = -50<BR>\n" );
document.write( ";<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Find a using the 1st equation, replace a with -50<BR>\n" );
document.write( "25a + 5b = 8750<BR>\n" );
document.write( "25(-50) + 5b = 8750<BR>\n" );
document.write( "-1250 = 5b = 8750<BR>\n" );
document.write( "5b = 8750 + 1250<BR>\n" );
document.write( "5b = 10000<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2F5 ALIGN=MIDDLE  ALT=\"10000%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 2000<BR>\n" );
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document.write( "The quadratic function (lb of beef for No. of cattle): f(x) = -50x^2 + 2000x<BR>\n" );
document.write( ";<BR>\n" );
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document.write( "Check solution using x=10<BR>\n" );
document.write( "y = -50(10^2) + 2000(10)<BR>\n" );
document.write( "y = -50(100) + 20000<BR>\n" );
document.write( "y = -5000 + 20000<BR>\n" );
document.write( "y = 15000 as given in the problem<BR>\n" );
document.write( " </SPAN>\n" );
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