document.write( "Question 87158: x varies directly as y and inversely as the square of z. If x=10 when y=8 and z=2, find x when y=12 and z=3. \n" ); document.write( "
Algebra.Com's Answer #63124 by Edwin McCravy(20054) $\"\"$ $\"About$
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document.write( "x varies directly as y and inversely as the square of z. If x=10 when y=8 and\r\n" );
document.write( "z=2, find x when y=12 and z=3.\r\n" );
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document.write( "Formula:\r\n" );
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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 x.\r\n" );
document.write( "There is one \"directly\" variable, y\r\n" );
document.write( "There is one \"inversely\" variable, z²\r\n" );
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document.write( "Substituting\r\n" );
document.write( "                      y\r\n" );
document.write( "               x = k·----\r\n" );
document.write( "                      z²\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( "x=10, y=8, z=2\r\n" );
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document.write( "                      8\r\n" );
document.write( "              10 = k·----\r\n" );
document.write( "                      2²\r\n" );
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document.write( "Solve for k\r\n" );
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document.write( "                      8\r\n" );
document.write( "              10 = k·---\r\n" );
document.write( "                      4    \r\n" );
document.write( "                \r\n" );
document.write( "                      \r\n" );
document.write( "              10 = k·2\r\n" );
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document.write( "              10 = 2k\r\n" );
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document.write( "                5 = k\r\n" );
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document.write( "Now substitute k = 5 into:\r\n" );
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document.write( "                      y\r\n" );
document.write( "               x = k·----\r\n" );
document.write( "                      z²\r\n" );
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document.write( "which gives:\r\n" );
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document.write( "                      y\r\n" );
document.write( "               x = 5·----\r\n" );
document.write( "                      z²\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 x\r\n" );
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document.write( "Substitute y=12 and z=3 into\r\n" );
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document.write( "                      y\r\n" );
document.write( "               x = 5·----\r\n" );
document.write( "                      z²\r\n" );
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document.write( "                      12\r\n" );
document.write( "               x = 5·----\r\n" );
document.write( "                      3²\r\n" );
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document.write( "                      12\r\n" );
document.write( "               x = 5·----\r\n" );
document.write( "                       9\r\n" );
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document.write( "3 divides into 9 to give 3 and into 12 to give 4:\r\n" );
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document.write( "                       4\r\n" );
document.write( "                      12\r\n" );
document.write( "               x = 5·----\r\n" );
document.write( "                       9\r\n" );
document.write( "                       3\r\n" );
document.write( "                           \r\n" );
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document.write( "                      4\r\n" );
document.write( "               x = 5·---\r\n" );
document.write( "                      3\r\n" );
document.write( "                \r\n" );
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document.write( "                    20\r\n" );
document.write( "               x = ----\r\n" );
document.write( "                     3\r\n" );
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document.write( "               x = 6\r\n" );
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document.write( "Edwin
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