document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1057214>Question 1057214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey Guys, \r<BR>\n" );
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document.write( "came across this problem in my maths homework and I can't seem to solve it. <BR>\n" );
document.write( "Can someone maybe help me out? \r<BR>\n" );
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document.write( "A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the width of the rectangle. Find the dimensions w * h of the Norman window whose perimeter is 500in. that has maximal area. \r<BR>\n" );
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document.write( "Answer in inches: \r<BR>\n" );
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document.write( "w= \r<BR>\n" );
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document.write( "h= \r<BR>\n" );
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document.write( "There is also a picture with it. \r<BR>\n" );
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document.write( "http://imgur.com/a/dr4ti\r<BR>\n" );
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document.write( "Thanks for the help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #672304 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=672304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle exactly matches the width of the rectangle. Find the dimensions w * h of the Norman window whose perimeter is 500in. that has maximal area. <BR>\n" );
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document.write( "Perimeter P = w + w*pi/2 + 2h = 500<BR>\n" );
document.write( "w*(pi/2 + 1) + 2h = 500<BR>\n" );
document.write( "h = 250 - w*(pi/4 + 1/2)<BR>\n" );
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document.write( "Area = w*h + pi*(w/2)^2/2<BR>\n" );
document.write( "Sub for h<BR>\n" );
document.write( "Area = w*(250 - w*(pi/4 + 1/2)) + pi*w^2/8<BR>\n" );
document.write( "Area = (pi/8)*w^2 -w^2*(pi/4 + 1/2) + 250w<BR>\n" );
document.write( "Area = (-pi/8 - 1/2)*w^2 + 250w<BR>\n" );
document.write( "dArea/dw = (-pi/4 - 1)w + 250 = 0<BR>\n" );
document.write( "w = 250/(pi/4 + 1)<BR>\n" );
document.write( "w =~ 140.025<BR>\n" );
document.write( "h =~ 70.012 </SPAN>\n" );
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