document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=282351>Question 282351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the radius of a circle is increased so that it is 5 centimeters less than twice the original radius, the area is increased by 32&#960; square centimeters. What is the original radius?\r<BR>\n" );
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document.write( "a 3   b 1/3   c 7   d &#960;/3  e 3&#960; <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 #205001 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=205001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r equal the original radius.\r<BR>\n" );
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document.write( "The new radius is equal to 2r - 5\r<BR>\n" );
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document.write( "Let a equal the original area.\r<BR>\n" );
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document.write( "The new area is equal to a + 32*pi\r<BR>\n" );
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document.write( "The original area is given by the formula:\r<BR>\n" );
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document.write( "a = pi * r^2\r<BR>\n" );
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document.write( "The new area is given by the formula\r<BR>\n" );
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document.write( "a + 32 * pi = pi * (2r - 5)^2\r<BR>\n" );
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document.write( "Replace a with the equivalent expression of pi*r^2 and you get:\r<BR>\n" );
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document.write( "pi*r^2 + 32*pi = pi*(2r-5)^2\r<BR>\n" );
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document.write( "Simplify to get:\r<BR>\n" );
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document.write( "pi*r^2 + 32*pi = 4*pi*r^2 - 20*pi*r + 25*pi\r<BR>\n" );
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document.write( "Divide both sides of this equation by pi to get:\r<BR>\n" );
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document.write( "r^2 + 32 = 4r^2 - 20r + 25\r<BR>\n" );
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document.write( "Subtract r^2 + 32 from both sides of this equation to get:\r<BR>\n" );
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document.write( "3r^2 - 20r - 7 = 0\r<BR>\n" );
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document.write( "This factors out to be (3r+1) * (r-7) = 0\r<BR>\n" );
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document.write( "This makes r = -1/3 and r = 7\r<BR>\n" );
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document.write( "r can't be negative so the answer is r = 7.\r<BR>\n" );
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document.write( "that would be selection c.\r<BR>\n" );
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document.write( "Plug this value into the original equation and you get:\r<BR>\n" );
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document.write( "a = pi * r^2 becomes a = pi * 49 which becomes a = 49*pi.\r<BR>\n" );
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document.write( "The new radius is equal to 2r - 5 which makes the new radius equal to 14 - 5 which makes the new radius equal to 9.\r<BR>\n" );
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document.write( "a = pi * 9^2 becomes a = pi * 81 becomes a = 81*pi\r<BR>\n" );
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document.write( "81*pi - 49*pi = 32*pi satisfying the requirements of the problem that states that when the radius is increased from 7 to 9, the area is increased by 32*pi.\r<BR>\n" );
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document.write( "9 = 2*7 - 5 = 14 - 5 = 9 which is true, confirming the radius increase.\r<BR>\n" );
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document.write( "81*pi - 49*pi = 32*pi conforming the area increase. </SPAN>\n" );
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