document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68456>Question 68456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Norman window is in the shape of a rectangle surmounted by a semicircle, as shown in the figure. Assume that the perimeter of the window is 32 feet. Express the area of the window as a function of r, the radius of the semicircle. Write your answer using function notation and simplify the function to three terms. Leave pi in its exact form. <BR>\n" );
document.write( "   I'm having diffficulty setting this problem up could you assist me. Any help is greatly appreciated. <BR>\n" );
document.write( "Thanks, <BR>\n" );
document.write( "Bridget </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48749 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=48749\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Norman window is in the shape of a rectangle surmounted by a semicircle, as shown in the figure. Assume that the perimeter of the window is 32 feet. Express the area of the window as a function of r, the radius of the semicircle. Write your answer using function notation and simplify the function to three terms. Leave pi in its exact form. <BR>\n" );
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document.write( "We know the width of the window is 2r:<BR>\n" );
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document.write( "The area of this shaped window would be:<BR>\n" );
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document.write( "Half the area of a circle + area of the rectangle:<BR>\n" );
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document.write( ".5(pi*r^2) + (2r * h) (height of the window)<BR>\n" );
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document.write( "We have to find the value of h in terms of r, using the given perimeter:<BR>\n" );
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document.write( "Circumference is pi*d so half a circumference would be pi*r<BR>\n" );
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document.write( "Perimeter equals:<BR>\n" );
document.write( " the width + twice the height + half the circumference:<BR>\n" );
document.write( " 2r + 2h + pi*r = 32<BR>\n" );
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document.write( " 2h = 32 - 2r - pi*r<BR>\n" );
document.write( " 2h = 32 - r(2+pi)<BR>\n" );
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document.write( "Divide equation by 2:<BR>\n" );
document.write( "  h = 16 - .5r(2+pi)<BR>\n" );
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document.write( "Substitute [16 - .5r(2+pi)] for h in the area equation:<BR>\n" );
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document.write( "A = .5(pi*r^2) + (2r * h)<BR>\n" );
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document.write( "A = .5(pi*r^2) + 2r[16-.5r(2+pi)]<BR>\n" );
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document.write( "A = .5*pi*r^2 + 32r - r^2(2+pi)<BR>\n" );
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document.write( "A = .5*pi*r^2 + 32r - 2r^2 - pi*r^2<BR>\n" );
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document.write( "A = .5*pi*r^2 - pi*r^2 + 32r - 2r^2; combine like terms<BR>\n" );
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document.write( "A = -.5*pi*r^2 - 2r^2 + 32r; should be give the area as a function of r<BR>\n" );
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document.write( "Check the perimeter if r = 4, remember 2h = 32 - 2r - pi*r<BR>\n" );
document.write( "Find 2h: 2h = 32 - 8 - 12.57 = 11.43<BR>\n" );
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document.write( "Perimeter<BR>\n" );
document.write( "2r + 2h + pi*r = 32<BR>\n" );
document.write( "8 + 11.43 + 12.57 = 32: proves our equation will work for a given r<BR>\n" );
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document.write( "Did this help? </SPAN>\n" );
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