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### Question

If z varies directly as the square of x and inversely as the square of y, and z is 3 when x is 6 and y is 16, find z when x is 12 and y is 25

### Answer #1 for Questions: If z varies directly as the square of x and inversely as the square of y, and z is 3 when x is 6 and y is 16, find z when x is 12 and y is 25

z = k*x^2

z = k*(1/y^2)

z = k(x^2/y^2) — gen. eqn.

@ z = 3, x = 6, y = 16, solve for k.

3 = k(6^2/16^2)

3*16^2/6^2 = k

k = 64/3

@ x = 12, y = 25

z = (64/3)*(12^2/25^2)

z = 3072/625 —- answer

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