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Question

Y varies directly as x and inversely as the square of z. Y=32 when x =36 and z=3. Find y when x =3 and z=12.

Answer 1

"y varies directly as x" means y = k₁x (where k₁ is the constant of proportionality). Since y = 32 when x = 36 we can say 32 = 36k₁ or k₁ = 32/36 = 8/9.

Therefore the basic equation relating x and y is y = (8/9)x. When x = 3, then y = 24/9

"y varies inversely as the square of z" means y = k₂/z² (where k₂ is the constant of proportionality). Since y = 32 when z = 3, we can say 32 = k₂/3² or k₂ = 32*9 = 288.

Therefore the basic equation relating z and y is y = 288/z². When z = 12, then y = 2