document.write( "Question 1058213: z varies directly as x^3 and inversely as y^3.
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\n" ); document.write( "(Round off your answer to the nearest hundredth.) \n" ); document.write( "
Algebra.Com's Answer #673303 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
z varies directly as x^3 and inversely as y^3.
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\n" ); document.write( "find z if x = 9 and y = 3.
\n" ); document.write( "(Round off your answer to the nearest hundredth.)\r
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document.write( "Formula:\r\n" );
document.write( "                       \r\n" );
document.write( "                       \"directly\" variable (or product of \"jointly\" variables)\r\n" );
document.write( "                         (if no directly or jointly variables, write 1 here)\r\n" );
document.write( "\"Varying\" quantity = k·---------------------------------------------------------\r\n" );
document.write( "                      \"inversely\" variable (or product of \"inversely variables\")\r\n" );
document.write( "                        (If no inversely variable(s), write 1 here)\r\n" );
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document.write( "The \"varying\" quantity is z.\r\n" );
document.write( "There is one \"directly\" variable, x³\r\n" );
document.write( "There is one \"inversely\" variable, y³\r\n" );
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document.write( "Substituting\r\n" );
document.write( "                      x³\r\n" );
document.write( "               z = k·----\r\n" );
document.write( "                      y³\r\n" );
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document.write( "Substituting the complete set of data, \r\n" );
document.write( "where ALL the variables are given:\r\n" );
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document.write( "z=184, x=10, y=6\r\n" );
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document.write( "                      10³\r\n" );
document.write( "             184 = k·-----\r\n" );
document.write( "                      6³\r\n" );
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document.write( "                      1000\r\n" );
document.write( "             184 = k·-----\r\n" );
document.write( "                       216\r\n" );
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document.write( "Reduce 1000/216 to 125/27\r\n" );
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document.write( "                      125\r\n" );
document.write( "             184 = k·-----\r\n" );
document.write( "                       27\r\n" );
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document.write( "Solve for k. Multiply through by 27\r\n" );
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document.write( "                      \r\n" );
document.write( "            4968 = k·125\r\n" );
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document.write( "            4968\r\n" );
document.write( "            ---- = k\r\n" );
document.write( "             125 \r\n" );
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document.write( "                       \r\n" );
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document.write( "Now substitute k = 4968/125 into:\r\n" );
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document.write( "                      x³\r\n" );
document.write( "               z = k·----\r\n" );
document.write( "                      y³\r\n" );
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document.write( "which gives:\r\n" );
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document.write( "                   4968  x³ \r\n" );
document.write( "               z = ----·----\r\n" );
document.write( "                    125  y³\r\n" );
document.write( "                      \r\n" );
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document.write( "Now substitute the second set of data,\r\n" );
document.write( "and solve for the missing letter z\r\n" );
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document.write( "Substitute x=9 and y=3 into\r\n" );
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document.write( "                   4968  x³ \r\n" );
document.write( "               z = ----·----\r\n" );
document.write( "                    125  y³\r\n" );
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document.write( "                   4968  9³ \r\n" );
document.write( "               z = ----·----\r\n" );
document.write( "                    125  3³\r\n" );
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document.write( "We grab the calculator and get\r\n" );
document.write( "                           \r\n" );
document.write( "               z = 1073.088\r\n" );
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document.write( "Round to the nearest hundredth:\r\n" );
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document.write( "               z = 1073.09\r\n" );
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document.write( "Edwin
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