document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200005>Question 200005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a farmer has 500m of fencing to build a rectangular enclosure along a river.No fencing is needed along the riverbank.what would be the maximum area enclosed by the fence?what would be the equation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150409 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=150409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a farmer has 500m of fencing to build a rectangular enclosure along a river.No fencing is needed along the riverbank.what would be the maximum area enclosed by the fence?what would be the equation?<BR>\n" );
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document.write( "Area = length*width<BR>\n" );
document.write( "2 sides are the width, one is length<BR>\n" );
document.write( "500 = l + 2w --> l = 500-2w<BR>\n" );
document.write( "Area = l*w<BR>\n" );
document.write( "Sub for w<BR>\n" );
document.write( "A = w*(500-2w)<BR>\n" );
document.write( "A = 500w - 2w^2  ***** That's the equation<BR>\n" );
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document.write( "Method 1<BR>\n" );
document.write( "Set the 1st derivate to zero<BR>\n" );
document.write( "0 = 500 - 4w<BR>\n" );
document.write( "w = 125<BR>\n" );
document.write( "l = 250<BR>\n" );
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document.write( "Method 2:<BR>\n" );
document.write( "A = 500w - 2w^2<BR>\n" );
document.write( "2w^2 - 500w + A = 0<BR>\n" );
document.write( "This is a parabola.  The max is at the vertex.<BR>\n" );
document.write( "The vertex is at w = -b/2a<BR>\n" );
document.write( "w = -b/2a = 500/4<BR>\n" );
document.write( "w = 125<BR>\n" );
document.write( "l = 250<BR>\n" );
document.write( "same as above.<BR>\n" );
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document.write( "Area = 125*250 = 31,250 sq meters.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );