document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203907>Question 1203907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a norman windo with a perimeter of 20 units has the shape of rectangle surmounted by a semi-circle. If its base is x units long and the height of the rectangle is y units long, write a mathematical model for its area in terms of x.<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 #839807 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a norman windo with a perimeter of 20 units has the shape of rectangle surmounted by a semi-circle. If its base is x units long and the height of the rectangle is y units long, write a mathematical model for its area in terms of x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=mananth&illustration_name=norman.png\">.\r<BR>\n" );
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document.write( "P=20 , base =x , height = y\r<BR>\n" );
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document.write( "base = x so radius of semicicle = x/2\r<BR>\n" );
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document.write( "Perimeter P  of semi circle = pi* (x/2) \r<BR>\n" );
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document.write( "Perimeter of window = x+2y++pi*(x/2)\r<BR>\n" );
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document.write( "20 - x-(pi x/2 )=2y\r<BR>\n" );
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document.write( "divide by 2\r<BR>\n" );
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document.write( "10-x/2-(pix)/4=y\r<BR>\n" );
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document.write( "10- (2x+pix)/4 =y\r<BR>\n" );
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document.write( "Area of window = area of semicircle + area of rectangle\r<BR>\n" );
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document.write( "radius of circle = x/2 area of semicircle - pix^2/8\r<BR>\n" );
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document.write( "A= pix^2/8+ xy ( after this step it just simplification)\r<BR>\n" );
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document.write( "A = pix^2/8 +x*(10- (2x+pix)/4)\r<BR>\n" );
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document.write( "pix^2/8 +10x -2x^2/4 -pix^2/4\r<BR>\n" );
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document.write( "(pix^2 +80x -4x^2-2pix^2)/8\r<BR>\n" );
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document.write( "(80x -4x^2-pix^2)/8\r<BR>\n" );
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document.write( "(80x- x^2(4+pi))/8\r<BR>\n" );
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