document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956610>Question 956610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that y is directly proportional to the cube of x and inversly proportional to the square of z, if x decreases by 35.9% and z increases by 5.8%, by what factor does y change? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584435 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=584435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "y = k * x^3 / z^2\r<BR>\n" );
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document.write( "when x decreased by 35.9%, then the value of x becomes x - .359 * x which is equal to .641 * x.\r<BR>\n" );
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document.write( "when z increased by 5.8%, then the value of z becomes z + .058 * z which is equal to 1.058 * z.\r<BR>\n" );
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document.write( "the new equation becomes:\r<BR>\n" );
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document.write( "y = k * (.641 * x)^3 / (1.058 * z)^2\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "y = (k * .641^3 * x^3) / (1.058^2 * x^2)\r<BR>\n" );
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document.write( "this is the same as:\r<BR>\n" );
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document.write( "y = (.641^3 / 1.058^2) * k * (x^3 / z^2)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "y = (.2352896118 * k * x^3) / z^2\r<BR>\n" );
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document.write( "y changes by a factor of .2352896118.\r<BR>\n" );
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document.write( "let's do an example to see if this holds true.\r<BR>\n" );
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document.write( "let x = 9 and let z = 5\r<BR>\n" );
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document.write( "when this happens, y is equal to 87.48\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "87.48 = k * 9^3 / 5^2\r<BR>\n" );
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document.write( "solve for k to get k = 3.\r<BR>\n" );
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document.write( "k is the constant of variation and so never changes.\r<BR>\n" );
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document.write( "now let y = k * (.641 * x)^3 / (1.058 * z)^2\r<BR>\n" );
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document.write( "when x = 9 and when z = 5 and when k = 3, this equation becomes:\r<BR>\n" );
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document.write( "y = (3 * (.641 * 9)^3) / (1.058 * 5)^2\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "y = (3 * 5.769^3) / 5.29^2 which becomes:\r<BR>\n" );
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document.write( "y = 20.58313524\r<BR>\n" );
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document.write( "the original value of y was 87.48\r<BR>\n" );
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document.write( "the new value of y is 20.58313524\r<BR>\n" );
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document.write( "the new value of y divided by the original value of y is equal to 20.58313524 / 87.48 which is equal to .2352896118.\r<BR>\n" );
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document.write( "the new value of y is equal to .2352896118 times the original value of y.\r<BR>\n" );
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document.write( "i believe that's what you are looking for.\r<BR>\n" );
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document.write( "that's the factor that the value of y was changed by.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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