document.write( "Question 1059524: z varies directly as x^2 and inversely as y^2 . If z = 165 when x = 4 and y = 7 , find z if x = 9 and y = 6 . (Round off your answer to the nearest hundredth.) \n" ); document.write( "
Algebra.Com's Answer #674556 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
z varies directly as x^2 and inversely as y^2 . If z = 165
\n" ); document.write( "when x = 4 and y = 7 , find z if x = 9 and y = 6 . (Round
\n" ); document.write( "off your answer to the nearest hundredth.)
\n" ); document.write( "
\r\n" );
document.write( "For all proportion problems, start with this:\r\n" );
document.write( "\r\n" );
document.write( "Varying           \"directly\" or product of \"jointlys\" or 1 if none \r\n" );
document.write( "quantity  = k · ----------------------------------------------------------\r\n" );
document.write( "                inversely variable or product of \"inverselys\" or 1 if none\r\n" );
document.write( "\r\n" );
document.write( "In this problem the varying quantity is z.\r\n" );
document.write( "We have one \"directly\", x².  We have one inversely, y².  So we have x² \r\n" );
document.write( "on top and y² on the bottom:\r\n" );
document.write( "\r\n" );
document.write( "z = k·\"x%5E2%2Fy%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "one set of values is
z = 165 when x = 4 and y = 7
\r\n" );
document.write( "\r\n" );
document.write( "Substitute these values:\r\n" );
document.write( "\r\n" );
document.write( "165 = k·\"4%5E2%2F7%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "165 = k·\"16%2F49\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \"49%2F16\"\r\n" );
document.write( "\r\n" );
document.write( "\"8085%2F16\" = k\r\n" );
document.write( "\r\n" );
document.write( "Now substitute \"8085%2F16\" for k in the first equation:\r\n" );
document.write( "\r\n" );
document.write( "z = k·\"x%5E2%2Fy%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "z = \"8085%2F16\"·\"x%5E2%2Fy%5E2\"\r\n" );
document.write( "\r\n" );
document.write( ">>...find z  if x = 9  and y = 6 ...<<\r\n" );
document.write( "\r\n" );
document.write( "Substitute those values\r\n" );
document.write( "\r\n" );
document.write( "z = \"8085%2F16\"·\"9%5E2%2F6%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "z = \"8085%2F16\"·\"81%2F36\"\r\n" );
document.write( "\r\n" );
document.write( "z = 1136.953125\r\n" );
document.write( "\r\n" );
document.write( "Round to\r\n" );
document.write( "\r\n" );
document.write( "z = 1136.95\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );