document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=853677>Question 853677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is 35 feet, express the area, A, as a function of the width, x, of the window.\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 #514180 by </B><A HREF=/tutors/aboutme.mpl?userid=harpazo><B>harpazo(655)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=harpazo><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=harpazo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The diameter of the semicircle is equal to the width of the rectangle.  You'd still use the height in the calculations along the way.\r<BR>\n" );
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document.write( "If the height of the rectangle part was h and the width was x, then the perimeter would be <BR>\n" );
document.write( "(length of 3 rectangle sides) + (curved part from semicircle) = \r<BR>\n" );
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document.write( "(h+h+x) + ( (1/2) 2 &#960; r )<BR>\n" );
document.write( "(h+h+x) + ( &#960; r )<BR>\n" );
document.write( "(2h+x) + ( &#960; (x/2) ) = 35\r<BR>\n" );
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document.write( "You can use this to get h in terms of x, or vice versa.  Then plug it into the expression for area to get things in terms of width.\r<BR>\n" );
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document.write( "2h+x = 35 - &#960;(x/2)<BR>\n" );
document.write( "2h = 35 - &#960;(x/2) - w\r<BR>\n" );
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document.write( "h = 17.5 - &#960;(x/4) - (x/2)\r<BR>\n" );
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document.write( "The area would be\r<BR>\n" );
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document.write( "(area of rectangle) + (area of semicircle) = \r<BR>\n" );
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document.write( "h*x + ((1/2)&#960; r^2)<BR>\n" );
document.write( "h*x + ((1/2)&#960; (x/2)^2)<BR>\n" );
document.write( "h*x + (&#960; x^2)/8\r<BR>\n" );
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document.write( "Take the expression for h and plug it in here to get everything in terms of x.\r<BR>\n" );
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document.write( "[17.5 - &#960;(x/4) - (x/2)]x + (&#960; x^2)/8\r<BR>\n" );
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document.write( "A(x) = 17.5x-&#960;(x^2/4)-(x^2/2) +<BR>\n" );
document.write( "(&#960; x^2)/8\r<BR>\n" );
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document.write( ":)\r<BR>\n" );
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