document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172670>Question 1172670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Quantity z varies jointly as x and the cube of y. If z = 96 when x = 2 and y = 2, find z when x = 3 and y = 3.<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 #797765 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
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document.write( "(for tutor @ikleyn)....<br><BR>\n" );
document.write( "... varies jointly as x and the CUBE of y..<br><BR>\n" );
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document.write( "Tutor @ikleyn has provided a response showing one way (of many!) to approach a problem like this.<br><BR>\n" );
document.write( "Another common method is to determine the constant of variation from the given data...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+kxy%5E3 ALIGN=MIDDLE  ALT=\"z+=+kxy%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96+=+k%282%29%282%5E3%29+=+16k ALIGN=MIDDLE  ALT=\"96+=+k%282%29%282%5E3%29+=+16k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+96%2F16+=+6 ALIGN=MIDDLE  ALT=\"k+=+96%2F16+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "... and then evaluate the formula with that constant and the new data.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+6xy%5E3 ALIGN=MIDDLE  ALT=\"z+=+6xy%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+6%283%29%283%5E3%29+=+6%2881%29+=+486 ALIGN=MIDDLE  ALT=\"z+=+6%283%29%283%5E3%29+=+6%2881%29+=+486\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And here is the way I myself find easiest to use....<br><BR>\n" );
document.write( "z is 96 when x is 2 and y is 2.<BR>\n" );
document.write( "When x changes from 2 to 3, the value of z changes by a factor of 3/2.<BR>\n" );
document.write( "When y changes from 2 to 3, the value of z changes by a factor of (3/2)^3.<br><BR>\n" );
document.write( "The \"new\" value of z is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2896%29%283%2F2%29%283%2F2%29%5E3+=+96%2881%2F16%29+=+81%2A6+=+486 ALIGN=MIDDLE  ALT=\"%2896%29%283%2F2%29%283%2F2%29%5E3+=+96%2881%2F16%29+=+81%2A6+=+486\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Different students will find different methods more to their liking; try these different methods and find what \"works\" for you.<br> </SPAN>\n" );
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