SOLUTION: x varies directly as the square of y and inversely as z. When y6 and z=3, x=112. What is x when y=3 and z=3?

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Question 186950: x varies directly as the square of y and inversely as z. When y6 and z=3, x=112. What is x when y=3 and z=3?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"x varies directly as the square of y and inversely as z" translates to x=ky%5E2%2Fz (let me know if you need help with the translation)



x=ky%5E2%2Fz Start with the given equation.


112=k%286%29%5E2%2F3 Plug in y=6, z=3 and x=112


112%283%29=k%286%29%5E2 Multiply both sides by 3.


336=k%286%29%5E2 Multiply


336=k%2836%29 Square 6 to get 36


336%2F36=k Divide both sides by 36 to isolate 'k'.


28%2F3=k Reduce


So the constant is k=28%2F3


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So the equation is:


x=%28%2828%2F3%29y%5E2%29%2Fz


x=%28%2828%2F3%29%283%29%5E2%29%2F%283%29 Plug in k=28%2F3, y=3 and z=3


x=%28%2828%2F3%29%289%29%29%2F%283%29 Square 3 to get 9


x=28 Multiply and reduce