document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003124>Question 1003124</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The circumference of one wheel is 20m longer than of another wheel. The product of the 2 circumferences is 144300mm. Calculate the length of the 2 circumferences. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619918 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=619918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the circumference of one of the wheels = c meters.\r<BR>\n" );
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document.write( "the circumference of the other wheel = c + 20 meters.\r<BR>\n" );
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document.write( "since both wheels are measured in meters, then the product will be in square meters.\r<BR>\n" );
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document.write( "the product, however, is in square millimeters.\r<BR>\n" );
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document.write( "it needs to be converted to square meters.\r<BR>\n" );
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document.write( "since 1 square millimeter is equal to 1 square meter / 1,000,000, then 144300 square millimters is equal to 144300 square millimmeters / 1,000,000 = .1443 square meters.\r<BR>\n" );
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document.write( "you get c * (c + 20) = .1443 square meters.\r<BR>\n" );
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document.write( "simplify to get c^2 + 20c = .1443 square meters.\r<BR>\n" );
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document.write( "subtract .1443 from both sides of the equation to get:\r<BR>\n" );
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document.write( "c^2 + 20c - .1443 = 0\r<BR>\n" );
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document.write( "solve this quadratic to get:\r<BR>\n" );
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document.write( "c = -20.0072124 meters or c = .0072124 meters\r<BR>\n" );
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document.write( "since c can't be negative, c must be equal to .0072124 meters\r<BR>\n" );
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document.write( "if c = .0072124 meters, then c + 20 = 20.0072124 meters\r<BR>\n" );
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document.write( ".0072124 meters * 20.0072124 meters = .1443 square meters.\r<BR>\n" );
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document.write( "this agrees with what the product should be, so c must be a good solution.\r<BR>\n" );
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document.write( "if you wanted to convert everything back to millimeters and square millimeters, you would then do the following.\r<BR>\n" );
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document.write( ".0072124 meters * 1000 = 7.2124 millimeters.\r<BR>\n" );
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document.write( ".0072124 meters * 1000 = 20007.2124 millimeters.\r<BR>\n" );
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document.write( "7.2124 millimeters * 20007.2124 millimeters = 144300.0187 square millimeters.\r<BR>\n" );
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document.write( "the difference between that and 144300 square millimeters is in the rounding.\r<BR>\n" );
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document.write( "what's shown as .0072124 meters is really 0.0072123990649864 meters rounded to 7 decimal digits.\r<BR>\n" );
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document.write( "if you use the numbers before they were rounded, you should get much closer to 144300.\r<BR>\n" );
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document.write( "i did and i got 144300 exactly.\r<BR>\n" );
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document.write( "if you have the capability, the recommendation is alwsys to use the unrounded numbers for all intermediate operations and then round for the final result only.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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