document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=327684>Question 327684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \" A Norman window is a rectangle with a semicircle on top. Big Sky window is designing a Norman window that will require 24 feet of trim. What dimensions will allow the maximum amount of light to enter the house?\"\r<BR>\n" );
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document.write( "I'm really lost on this one. Thank you for your time.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #234708 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=234708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the height of the rectangular part be y and the radius of the semi-circular part be r.  Therefore, the perimeter of the window is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=pi%2Ar%2B2y%2B2r=24 ALIGN=MIDDLE  ALT=\"S=pi%2Ar%2B2y%2B2r=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2824-2r-pi%2Ar%29%2F2 ALIGN=MIDDLE  ALT=\"y=%2824-2r-pi%2Ar%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=pi%2Ar%5E2%2F2%2B2ry ALIGN=MIDDLE  ALT=\"A=pi%2Ar%5E2%2F2%2B2ry\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Sub y into A and it simplifies down to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-pi%2Ar%5E2%2F2-2r%5E2%2B24r=-%28pi%2F2%2B2%29r%5E2%2B24r ALIGN=MIDDLE  ALT=\"A=-pi%2Ar%5E2%2F2-2r%5E2%2B24r=-%28pi%2F2%2B2%29r%5E2%2B24r\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is what must be maximized to allow the most light in.\r<BR>\n" );
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document.write( "It can be done with or without calculus. You did not specify.\r<BR>\n" );
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document.write( "To find the max without calc, we can use the formula for the vertex of a parabola, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"r=-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using this we find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=24%2F%28pi%2B4%29 ALIGN=MIDDLE  ALT=\"r=24%2F%28pi%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This can be subbed into the y equation above to find the y dimension and thus the area needed to maximize light entry.\r<BR>\n" );
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