document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286594>Question 286594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular garden is enclosed so that the river borders 1 side and 300m of fencing are used for the other 3 sides.\r<BR>\n" );
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document.write( "a)What is the formula for the area in terms of x and y?<BR>\n" );
document.write( "b)What is the formul that relates x and y to the perimeter?<BR>\n" );
document.write( "c)Write a formulaa for the area in terms of x only<BR>\n" );
document.write( "d)What are the dimensions of the garden if the area is a maximum? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207878 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=207878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the length of the side bordering the river = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let the 2 sides perpendicular to the side bordering the river = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given:<BR>\n" );
document.write( "a)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+xy ALIGN=MIDDLE  ALT=\"A+=+xy\"   DISABLED_style= \"max-width:90%; height:auto;\" > m2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P+=+300+%2B+y ALIGN=MIDDLE  ALT=\"P+=+300+%2B+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+2x+%2B+2y ALIGN=MIDDLE  ALT=\"P=+2x+%2B+2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+300+-+y ALIGN=MIDDLE  ALT=\"2x+=+300+-+y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+300+-+2x ALIGN=MIDDLE  ALT=\"y+=+300+-+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+x%2A%28300+-+2x%29 ALIGN=MIDDLE  ALT=\"A+=+x%2A%28300+-+2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+300x+-+2x%5E2 ALIGN=MIDDLE  ALT=\"A+=+300x+-+2x%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 ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a maximum halfway between the 2 roots. First I'll find the roots<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%282x+-+300%29+=+0 ALIGN=MIDDLE  ALT=\"x%2A%282x+-+300%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+300+=+0 ALIGN=MIDDLE  ALT=\"2x+-+300+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+300 ALIGN=MIDDLE  ALT=\"2x+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+150 ALIGN=MIDDLE  ALT=\"x+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The midpoint is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+75 ALIGN=MIDDLE  ALT=\"x+=+75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+300+-+2x ALIGN=MIDDLE  ALT=\"y+=+300+-+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+300+-+150 ALIGN=MIDDLE  ALT=\"y+=+300+-+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+150 ALIGN=MIDDLE  ALT=\"y+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d)The dimensions that maximize area are 75 x 150<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "Just vary the dimensions a little bit, and Area should decrease<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+75%2A150 ALIGN=MIDDLE  ALT=\"A+=+75%2A150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+11250 ALIGN=MIDDLE  ALT=\"A+=+11250\"   DISABLED_style= \"max-width:90%; height:auto;\" > m2<BR>\n" );
document.write( "Suppose:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A2+=+76%2A148 ALIGN=MIDDLE  ALT=\"A2+=+76%2A148\"   DISABLED_style= \"max-width:90%; height:auto;\" > -note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A76+%2B+148+=+152+%2B+148 ALIGN=MIDDLE  ALT=\"2%2A76+%2B+148+=+152+%2B+148\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=152%2B+148+=+300 ALIGN=MIDDLE  ALT=\"152%2B+148+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" >  as it should<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A2+=+11248 ALIGN=MIDDLE  ALT=\"A2+=+11248\"   DISABLED_style= \"max-width:90%; height:auto;\" > It decreased by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );