Y varies directly as x and inversely as the square of z. y=8 when x=16 and z=4. Find y when x=3 and z=9.

The value of y is

Explanation:

Given that y varies directly as x and inversely as the square of z.

Thus, it can be written as

Also, given that when and

Substituting these values in the above expression, we have,

Thus, the value of the constant is 8

Now, we shall find the value of y.

The value of y can be determined by substituting , and in the expression

Thus, we have,

Simplifying, we get,

Dividing, we get,

Thus, the value of y is