document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737399>Question 737399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A lifeguard is interested in enclosing a rectangular swimming area along the beach. The swimming area will be enclosed using 72m of floating rope and will be bordered on one side by the beach: that is the problem \r<BR>\n" );
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document.write( "these are the questions <BR>\n" );
document.write( "a. Draw a sketch to model the situation<BR>\n" );
document.write( "b. Find the dimensions (length and width) that provide the maximum area for swimming.<BR>\n" );
document.write( "c. What is the maximum area available for swimming?\r<BR>\n" );
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document.write( "Please could someone help me with this today  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450475 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=450475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A lifeguard is interested in enclosing a rectangular swimming area along the beach.<BR>\n" );
document.write( " The swimming area will be enclosed using 72m of floating rope and will be bordered on one side by the beach: that is the problem these are the questions<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a. Draw a sketch to model the situation<BR>\n" );
document.write( "I'll let you handle this<BR>\n" );
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document.write( "b. Find the dimensions (length and width) that provide the maximum area for swimming.<BR>\n" );
document.write( "Only 3 sides are required therefore<BR>\n" );
document.write( "L + 2W = 72<BR>\n" );
document.write( "L = (72-2W)<BR>\n" );
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document.write( "c. What is the maximum area available for swimming?<BR>\n" );
document.write( "A = L * W<BR>\n" );
document.write( "Replace L with (72-2W)<BR>\n" );
document.write( "A = W(72-2W)<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "A = -2W^2 + 72W<BR>\n" );
document.write( "Max area occurs on the axis of symmetry, find it using formula: x = -b/(2a)<BR>\n" );
document.write( "W = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-72%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"%28-72%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "W = 18 m is the width that gives max area<BR>\n" );
document.write( "then<BR>\n" );
document.write( "L = 72 - 2(18) = 36 m is the length for max area<BR>\n" );
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document.write( "Actual max area: 18 * 36 = 648 sq/m<BR>\n" );
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document.write( "If you graph the equation you can see that max area occurs when x=18 (width)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+50%2C+-100%2C+700%2C+-2x%5E2%2B72x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+50%2C+-100%2C+700%2C+-2x%5E2%2B72x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </SPAN>\n" );
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