document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=399784>Question 399784</A>: <I><SPAN STYLE=\"word-break: break-all;\">   A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is 21 ft, find the dimensions of the window so that the greatest possible amount of light is admitted. \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #283190 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=283190\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Norman window has the shape of a rectangle surmounted by a semicircle.<BR>\n" );
document.write( " (Thus the diameter of the semicircle is equal to the width of the rectangle.)<BR>\n" );
document.write( " If the perimeter of the window is 21 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.<BR>\n" );
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document.write( "Let x = the width of the window and diameter of the semicircle<BR>\n" );
document.write( "Let h = height of the rectangular portion of the window<BR>\n" );
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document.write( "Perimeter:<BR>\n" );
document.write( "2h + x + .5x*pi = 21<BR>\n" );
document.write( "2h + 2.57x = 21<BR>\n" );
document.write( "2h = 21 - 2.57x<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2821-2.57x%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28%2821-2.57x%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = (10.5-1.285x)<BR>\n" );
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document.write( "What would be the window with the greatest area;<BR>\n" );
document.write( "Area = semicircle + rectangle<BR>\n" );
document.write( "Radius = .5x<BR>\n" );
document.write( "A = (.5*pi*(.5x)^2) + h*x<BR>\n" );
document.write( "Replace h with (10.5-1.285x<BR>\n" );
document.write( "A = (1.57*.25x^2) + x(10.5-1.285x)<BR>\n" );
document.write( "A = .3927x^2  - 1.285x^2 + 10.5x<BR>\n" );
document.write( "A = -.8923x^2 + 10.5x<BR>\n" );
document.write( "Find the max area by finding the axis of symmetry; x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10.5%29%2F%282%2A-.8923%29 ALIGN=MIDDLE  ALT=\"%28-10.5%29%2F%282%2A-.8923%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 5.88 meter is the width with the greatest area<BR>\n" );
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document.write( "Find the max area<BR>\n" );
document.write( "A = -.8923(5.88^2) + 10.5(5.88)<BR>\n" );
document.write( "A = -.8923(5.88^2) + 10.5(5.88)<BR>\n" );
document.write( "A = -30.85 + 61.74<BR>\n" );
document.write( "A = 30.89 sq/ft is max area </SPAN>\n" );
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