Question

If y varies directly as x and inversely as the square of z and y=6 when x=64 and z =8, how do you find y when x = 21 and z=2?

If y varies directly as x and inversely as the square of z and y=6 when x=64 and z =8, how do you find y when x = 21 and z=2?

Answer 1

`y=31 1/2`

Explanation:

For y to vary directly with x and inversely with the square of z, we can write `y=kx/z^2`

We are told that `6=k*64/8^2=k` i.e. `k=6`

Therefore `y=6x/z^2`
When `x=21, z=2` this gives us `y=6*21/2^2=63/2=31 1/2`

Incidentally your question is similar to https://socratic.org/questions/y-varies-directly-as-x-and-inversely-as-the-square-of-z-y-12-when-x-64-and-z-4-h