document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181262>Question 181262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help Please!!!!<BR>\n" );
document.write( "A rancher with 750ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.\r<BR>\n" );
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document.write( "a. Find a function that models the total area of the four pens.\r<BR>\n" );
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document.write( "b. Find the largest possible total area of the four pens. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #135951 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=135951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rancher with 750ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.<BR>\n" );
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document.write( "If you draw this, you can see that the fencing required:  2L + 5W = 750<BR>\n" );
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document.write( "a. Find a function that models the total area of the four pens.<BR>\n" );
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document.write( "Let x = the width<BR>\n" );
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document.write( "2L + 5x = 750<BR>\n" );
document.write( "2L = (750 - 5x)<BR>\n" );
document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28750-5x%29%2F2 ALIGN=MIDDLE  ALT=\"%28750-5x%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "L = (375 - 2.5x)<BR>\n" );
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document.write( "Area = x * L<BR>\n" );
document.write( "Substitute (375-2.5x) for L<BR>\n" );
document.write( "A = x*(375-2.5x)<BR>\n" );
document.write( "A = 375x - 2.5x^2<BR>\n" );
document.write( "the function that models the total area<BR>\n" );
document.write( "f(x) = -2.5x^2 + 375x<BR>\n" );
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document.write( "b. Find the largest possible total area of the four pens.<BR>\n" );
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document.write( "Since this is a quadratic equation, we can do this by finding the axis<BR>\n" );
document.write( "of symmetry, then find the vertex. Formula for that is: x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-375%29%2F%282%2A-2.5%29 ALIGN=MIDDLE  ALT=\"%28-375%29%2F%282%2A-2.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-375%29%2F%28-5%29 ALIGN=MIDDLE  ALT=\"%28-375%29%2F%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +75, the max area will be when width is 75 ft<BR>\n" );
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document.write( "Find the vertex (max area):<BR>\n" );
document.write( "A = -2.5(75^2) + 375(75)<BR>\n" );
document.write( "A = -2.5(5625) + 28125<BR>\n" );
document.write( "A = -14062.5 + 28125<BR>\n" );
document.write( "A = +14062.5 sq ft is the max area<BR>\n" );
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document.write( "Did this make sense to you, any questions?<BR>\n" );
document.write( " </SPAN>\n" );
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