Question

Y is directly proportional to x and inversely proportional to the square of z and y = 40 when x = 80 and z = 4, how do you find y when x = 7 and z = 16?

Answer 1

`y=7/32` when `x=7` and `z=16`

Explanation:

`y` being directly proportional to `x` and inversely proportional to the square of `z` means there is a constant `k` such that `y=kx/z^2=(kx)/z^2`.

Since `y=40` when `x=80` and `z=4`, it follows that `40=(80k)/4^2=5k` which implies `k=8`.

Therefore, `y=(8x)/z^2`.

Hence, when `x=7` and `z=16`, `y=56/16^2=7/(2*16)=7/32`.