Question

Need help !!on math problem

Answer 1

`A`.
`y^(2)` =
`(1)/(16)`
`x^(3)`

Explanation:

The statement "the square of
`y` varies directly as the cube of
`x`" can be expressed with the equation:

`y^(2)` =
`kx^(3)` ("
`k`" is the constant of variation)

Now, we can use the given values when
`x` =
`4` and
`y` =
`2` to find the value of

"
`k`":

`(2)^(2)` =
`k(4)^(3)`

`4` =
`64k`

Now, solve for "
`k`":

`k` =
`(4)/(64)`

`k` =
`(1)/(16)`

So, the equation for the relationship between
`x` and
`y` is:

`y^(2)` = (
`(1)/(16)`)
`x^(3)`

Therefore, the correct choice is:

`A`.
`y^(2)` =
`(1)/(16)x^(3)`