document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153414>Question 153414</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sam has 3000 feet of fencting available to enclose a rectangular field\r<BR>\n" );
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document.write( "a) Express the area  A  of the rectangle as a function of x where  x is the length of the rectangle.\r<BR>\n" );
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document.write( "b) For what value of x is the area largest?\r<BR>\n" );
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document.write( "c) What is the maximum area?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112966 by </B><A HREF=/tutors/aboutme.mpl?userid=orca><B>orca(409)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=orca><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=112966\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First we need to express the width of the rectangle in terms of x.<BR>\n" );
document.write( "The perimeter of the rectangle is:<BR>\n" );
document.write( "Perimeter = 2*length + 2*width.<BR>\n" );
document.write( "So width = (perimeter - 2*length)/2<BR>\n" );
document.write( "Substituting length = x and perimeter = 3000, we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width+=+%283000-2x%29%2F2=1500-x ALIGN=MIDDLE  ALT=\"width+=+%283000-2x%29%2F2=1500-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the area of the rectangle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=length%2Awidth ALIGN=MIDDLE  ALT=\"A=length%2Awidth\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%281500-x%29 ALIGN=MIDDLE  ALT=\"x%2A%281500-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500x-x%5E2%29 ALIGN=MIDDLE  ALT=\"1500x-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find the maximum value of the quadratic expression, we can use either the formula or the completing square method. Here the second method is used.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+1500x-x%5E2 ALIGN=MIDDLE  ALT=\"A+=+1500x-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B1500x ALIGN=MIDDLE  ALT=\"-x%5E2%2B1500x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%5E2-1500x%29 ALIGN=MIDDLE  ALT=\"-%28x%5E2-1500x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%5E2-2%2A750x%29 ALIGN=MIDDLE  ALT=\"-%28x%5E2-2%2A750x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%5E2-2%2A750x%2B750%5E2-750%5E2%29 ALIGN=MIDDLE  ALT=\"-%28x%5E2-2%2A750x%2B750%5E2-750%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%28x%5E2-2%2A750x%2B750%5E2%29-750%5E2%29 ALIGN=MIDDLE  ALT=\"-%28%28x%5E2-2%2A750x%2B750%5E2%29-750%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%28x-750%29%5E2-750%5E2%29 ALIGN=MIDDLE  ALT=\"-%28%28x-750%29%5E2-750%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-750%29%5E2%2B750%5E2 ALIGN=MIDDLE  ALT=\"-%28x-750%29%5E2%2B750%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%5E2-%28x-750%29%5E2 ALIGN=MIDDLE  ALT=\"750%5E2-%28x-750%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%5E2-%28x-750%29%5E2 ALIGN=MIDDLE  ALT=\"750%5E2-%28x-750%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has maximum value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%5E2 ALIGN=MIDDLE  ALT=\"750%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-750%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-750%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-750%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-750%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x must be equal to 750.<BR>\n" );
document.write( "So when x = 750, A has the maximum value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%5E2 ALIGN=MIDDLE  ALT=\"750%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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