document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=564767>Question 564767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that y varies directly as x and inversely as z^2. If x and z are both decreased by 20%, then y?\r<BR>\n" );
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document.write( "This is all I've got y=kx/z^2 ...I don't even know whether it's right. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #365471 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=365471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you problem states that y varies directly as x and inversely as z^2.<BR>\n" );
document.write( "the formula for that would be:<BR>\n" );
document.write( "y = kx/z^2<BR>\n" );
document.write( "you got started right because this agrees with what you showed.<BR>\n" );
document.write( "if x and y are each reduced by 20%, then you get:<BR>\n" );
document.write( "x - .2x = .8x<BR>\n" );
document.write( "z - .2z = .8z<BR>\n" );
document.write( "you would replace x with .8x and you would replace z with .8z to get:<BR>\n" );
document.write( "y = k(.8x)/(.8z)^2<BR>\n" );
document.write( "you would simplify this to:<BR>\n" );
document.write( "y = .8kx / .64z^2 which you can further simplify to:<BR>\n" );
document.write( "y = 1.25kx/z^2<BR>\n" );
document.write( "let's see how this would pan out.<BR>\n" );
document.write( "assume x = 64 and assume z = 8 and assume k = 1.<BR>\n" );
document.write( "that makes the math simple.<BR>\n" );
document.write( "your original equation of:<BR>\n" );
document.write( "y = kx/z^2 becomes:<BR>\n" );
document.write( "y = 1*64/8^2 which becomes:<BR>\n" );
document.write( "y = 64/64 which becomes:<BR>\n" );
document.write( "y = 1.<BR>\n" );
document.write( "now assume that x and y are both decreased by 20%.<BR>\n" );
document.write( "your equation of y = kx/z^2 becomes y = 1*(.8x) / (.8z)^2 which becomes:<BR>\n" );
document.write( "y = .8*64 / (.8*8)^2 which becomes:<BR>\n" );
document.write( "y = 51.2 / 6.4^2 which  becomes:<BR>\n" );
document.write( "y = 51.2 / 20.96 which becomes:<BR>\n" );
document.write( "y = 1.25<BR>\n" );
document.write( "we said that your equation became:<BR>\n" );
document.write( "y = 1.25kx/z^2<BR>\n" );
document.write( "since your original x = 64 and your original y = 8, this equation becomes:<BR>\n" );
document.write( "y = 1.25(64)/(8^2) which becomes:<BR>\n" );
document.write( "y = 80/64 which becomes:<BR>\n" );
document.write( "y = 1.25<BR>\n" );
document.write( "the answer comes out the same so the equation is good.<BR>\n" );
document.write( "your answer is:<BR>\n" );
document.write( "y = 1.25kx/z^2<BR>\n" );
document.write( "a good reference on this type of problem can be found here:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://regentsprep.org/Regents/math/algtrig/ATE7/indexATE7.htm\" target = \"_blank\">http://regentsprep.org/Regents/math/algtrig/ATE7/indexATE7.htm</a> </SPAN>\n" );
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