document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583502>Question 583502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE help me with this challenging problem!!!<BR>\n" );
document.write( "An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is to be 400 meters. Determine the radius of the semicircular ends of the track in terms of y.Use the result to write and equation in terms of x and y for the distance around the track. Use your result from that to write the area A  of the rectangular section as function of x.What dimensions for the rectangular region maximize the area (of the rectangular region)?  Do not attempt to maximize the area for the whole figure!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372503 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=372503\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance around the track is to be 400 meters. Determine the radius of the semicircular ends of the track in terms of y.Use the result to write and equation in terms of x and y for the distance around the track. Use your result from that to write the area A  of the rectangular section as function of x.What dimensions for the rectangular region maximize the area (of the rectangular region)?<BR>\n" );
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document.write( "No constraints are given.  The track could be circular, or the 2 straight sections almost 200 meters with small diameter circles.<BR>\n" );
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document.write( "If the center line of the track is parallel to the y-axis, x is the distance between the parallel straight sections, y = distance between the centers of the semi-circles:<BR>\n" );
document.write( "Cicumference = pi*x + 2y = 400 meters<BR>\n" );
document.write( "x = 2r<BR>\n" );
document.write( "r = x/2 = (400 - 2y)/2pi meters<BR>\n" );
document.write( "r = (200 - y)/pi meters<BR>\n" );
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document.write( "Rect area = x*y<BR>\n" );
document.write( "The rect area is a max @ x = y<BR>\n" );
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