document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194404>Question 194404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A norman window is one that consists of a rectangle with a curved top to it. the curved top is actually a semicircle that sits on top of the rectangle. if the perimeter around the norman window is 20 feet, what radius of the semicircle will provide the greatest window area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145874 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=145874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A norman window is one that consists of a rectangle with a curved top to it. <BR>\n" );
document.write( "the curved top is actually a semicircle that sits on top of the rectangle.<BR>\n" );
document.write( " if the perimeter around the norman window is 20 feet, what radius of the<BR>\n" );
document.write( " semicircle will provide the greatest window area?<BR>\n" );
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document.write( "Let H = the height of the rectangular portion of the window<BR>\n" );
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document.write( "Let x = the radius of the semi circle on top<BR>\n" );
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document.write( "Half the circumference = pi*x<BR>\n" );
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document.write( "Width of the window = 2x<BR>\n" );
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document.write( "The perimeter:<BR>\n" );
document.write( "2H + 2x + pix = 20<BR>\n" );
document.write( "Solve for H<BR>\n" );
document.write( "2H = 20 - 2x - pix <BR>\n" );
document.write( "H = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820-2x-pix%29%2F2 ALIGN=MIDDLE  ALT=\"%2820-2x-pix%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Area formula: A = (H*2x) + .5pi*x^2<BR>\n" );
document.write( "Replace H with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820-2x-pix%29%2F2 ALIGN=MIDDLE  ALT=\"%2820-2x-pix%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = 2x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820-2x-pi%2Ax%29%2F2 ALIGN=MIDDLE  ALT=\"%2820-2x-pi%2Ax%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\".5pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel the 2<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2820-2x-pi%2Ax%29 ALIGN=MIDDLE  ALT=\"x%2820-2x-pi%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >+ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.5pi%2Ax%5E2 ALIGN=MIDDLE  ALT=\".5pi%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x+-+2x%5E2+-+%28pix%5E2%29+%2B+%28.5pix%5E2%29 ALIGN=MIDDLE  ALT=\"20x+-+2x%5E2+-+%28pix%5E2%29+%2B+%28.5pix%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Leaving us with<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2+%2B+20x+-+.5pix%5E2 ALIGN=MIDDLE  ALT=\"-2x%5E2+%2B+20x+-+.5pix%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".5*pi = 1.57<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2+-+1.57x%5E2+%2B+20x ALIGN=MIDDLE  ALT=\"-2x%5E2+-+1.57x%5E2+%2B+20x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3.57x%5E2+%2B+20x ALIGN=MIDDLE  ALT=\"-3.57x%5E2+%2B+20x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A quadratic equation, find the vertex for max area; a=-3.57, b=20<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-20%29%2F%282%2A-3.57%29 ALIGN=MIDDLE  ALT=\"%28-20%29%2F%282%2A-3.57%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-20%29%2F%28-7.14%29 ALIGN=MIDDLE  ALT=\"%28-20%29%2F%28-7.14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 2.8 ft radius for max area<BR>\n" );
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document.write( "Check solution by finding the perimeter with this radius<BR>\n" );
document.write( "Find 2H<BR>\n" );
document.write( "2H = 20 - 2(2.8) - 2.8pi<BR>\n" );
document.write( "2H = 5.6 ft<BR>\n" );
document.write( "Find perimeter: <BR>\n" );
document.write( "2H + 2x + pix = 20<BR>\n" );
document.write( "5.6 + 2(2.8) + 2.8*pi = <BR>\n" );
document.write( "5.6 + 5.6 + 8.8 = 20<BR>\n" );
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document.write( "note that max area is when the rectangular portion, is a square, 5.6 by 5.6\r<BR>\n" );
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document.write( " </SPAN>\n" );
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