document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044598>Question 1044598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Considering the following problem:A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river . What are the dimensions of the largest area that he can fence?<BR>\n" );
document.write( "a. Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field.<BR>\n" );
document.write( "b. Find a function that models the area of the field in terms of one of its sides.<BR>\n" );
document.write( "c. Use your model to solve the problem, and compare with your answer to part (a). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660023 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=660023\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+ ALIGN=MIDDLE  ALT=\"+s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of one of  the sides which<BR>\n" );
document.write( "is perpendicular to the river<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2400+-+2s+ ALIGN=MIDDLE  ALT=\"+2400+-+2s+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the length of the side which <BR>\n" );
document.write( "is parallel to the river<BR>\n" );
document.write( "-------------------------------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+ ALIGN=MIDDLE  ALT=\"+A+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area of the rectangular field in square ft<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+s%2A%28+2400+-+2s+%29+ ALIGN=MIDDLE  ALT=\"+A+=+s%2A%28+2400+-+2s+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+-2s%5E2+%2B+2400s+ ALIGN=MIDDLE  ALT=\"+A+=+-2s%5E2+%2B+2400s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "If the form of the equation looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28s%29+=+a%2As%5E2+%2B+b%2As+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28s%29+=+a%2As%5E2+%2B+b%2As+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the s-value of the<BR>\n" );
document.write( "vertex of the parabola is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+s%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "In this case:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-2+ ALIGN=MIDDLE  ALT=\"+a+=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+2400+ ALIGN=MIDDLE  ALT=\"+b+=+2400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5Bv%5D+=+%28+-2400+%29+%2F+%28+2%2A%28-2%29+%29+ ALIGN=MIDDLE  ALT=\"+s%5Bv%5D+=+%28+-2400+%29+%2F+%28+2%2A%28-2%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5Bv%5D+=+600+ ALIGN=MIDDLE  ALT=\"+s%5Bv%5D+=+600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bv%5D+=+s%2A%28+2400+-+2s+%29+ ALIGN=MIDDLE  ALT=\"+A%5Bv%5D+=+s%2A%28+2400+-+2s+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bv%5D+=+600%2A%28+2400+-+1200+%29+ ALIGN=MIDDLE  ALT=\"+A%5Bv%5D+=+600%2A%28+2400+-+1200+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bv%5D+=+600%2A1200+ ALIGN=MIDDLE  ALT=\"+A%5Bv%5D+=+600%2A1200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bv%5D+=+720000+ ALIGN=MIDDLE  ALT=\"+A%5Bv%5D+=+720000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum area is 720,000 ft2<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Knowing this, you can try a slightly different <BR>\n" );
document.write( "shape for the rectangular field, say by making<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+598+ ALIGN=MIDDLE  ALT=\"+s+=+598+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2400+-+2s+=+2400+-+1196+ ALIGN=MIDDLE  ALT=\"+2400+-+2s+=+2400+-+1196+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2400+-+2s+=+1204+ ALIGN=MIDDLE  ALT=\"+2400+-+2s+=+1204+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+598%2A1204+ ALIGN=MIDDLE  ALT=\"+A+=+598%2A1204+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+719992+ ALIGN=MIDDLE  ALT=\"+A+=+719992+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is clearly a little less than the maximum area<BR>\n" );
document.write( "I just got<BR>\n" );
document.write( "Now try:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+602+ ALIGN=MIDDLE  ALT=\"+s+=+602+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2400+-+2s+=+2400+-+1204+ ALIGN=MIDDLE  ALT=\"+2400+-+2s+=+2400+-+1204+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2400+-+2s+=+1196+ ALIGN=MIDDLE  ALT=\"+2400+-+2s+=+1196+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+602%2A1196+ ALIGN=MIDDLE  ALT=\"+A+=+602%2A1196+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A+=+719992+ ALIGN=MIDDLE  ALT=\"+A+=+719992+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Also a little less than maximum area ( same number as before )<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Here's a plot of the equation for area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+400%2C+-250%2C+1500%2C+-80000%2C+800000%2C+-2x%5E2+%2B+2400x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+400%2C+-250%2C+1500%2C+-80000%2C+800000%2C+-2x%5E2+%2B+2400x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );