SOLUTION: If x varies as the square of y and inversely as z and x=12 when y=3 and z=6,find x when y=9 and z=6.

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Question 1149574: If x varies as the square of y and inversely as z and x=12 when y=3 and z=6,find x when y=9 and z=6.
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
If x varies as the square of y and inversely as z 
Whatever comes after "varies as" is multiplied by k and goes on top, 
and what comes after "inversely as" goes on the bottom.

matrix%281%2C3%2Cx%2C%22%22=%22%22%2C%28k%2Ay%5E2%29%2Fz%5E%22%22%29
and x=12 when y=3 and z=6,
Substitute and solve for k

matrix%281%2C3%2C12%2C%22%22=%22%22%2C%28k%2A%283%29%5E2%29%2F%286%29%5E%22%22%29%29

matrix%281%2C3%2C12%2C%22%22=%22%22%2C%28k%2A%289%29%29%2F6%29%29

matrix%281%2C3%2C12%2C%22%22=%22%22%2C9k%2F6%29

Multiply both sides by 6

matrix%281%2C3%2C72%2C%22%22=%22%22%2C9k%29

matrix%281%2C3%2C8%2C%22%22=%22%22%2Ck%29

Substitute 8 for k in the original variation equation:

matrix%281%2C3%2Cx%2C%22%22=%22%22%2C%288%2Ay%5E2%29%2Fz%5E%22%22%29
find x when y=9 and z=6.
Substitute the new values for y and z

matrix%281%2C3%2Cx%2C%22%22=%22%22%2C%288%2A9%5E2%29%2F6%5E%22%22%29

matrix%281%2C3%2Cx%2C%22%22=%22%22%2C%288%2A81%29%2F6%29

matrix%281%2C3%2Cx%2C%22%22=%22%22%2C108%29

Edwin