SOLUTION: ``Suppose z varies directly with x and inversely with the square of y. If z=12 when x=4 and y=4, what is z when x=8 and y=10? mph''.

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Question 1186202: ``Suppose z varies directly with x and inversely with the square of y. If z=12 when x=4 and y=4, what is z when x=8 and y=10?

mph''.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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z varies directly with x and inversely with the square of y. If z=12 when x=4 and y=4, what is,...
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k, variation constant

z=kx%2Fy%5E2

zy%5E2%2Fx=k
k=12%2A4%5E2%2F4
k=12%2A4
k=48
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highlight_green%28z=48%28x%2Fy%5E2%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If you need a formula to express the relationship between x, y, and z, then you can determine the constant of variation as the other tutor did. You would probably want to do that if you were going to use the formula for a large number of different parameter values.

But if you only need to solve the problem for the one set of new parameters, then you don't have to do all that work.

z varies directly as x; x changes from 4 to 8, an increase by a factor of 2; so z increases by a factor of 2.

z varies inversely as the square of y; y changes from 4 to 10, an increase by a factor of 5/2; so z decreases by a factor of (5/2)^2.

%2812%29%282%29%281%2F%285%2F2%29%5E2%29=24%284%2F25%29=96%2F25=3.84

ANSWER: When x = 8 and y = 10, z = 96/25 or z = 3.84