Question

If Y varies inversely as the cube root of x. If y = 4 when x = 27, how do you find y when x = 8?

Answer 1

y = 6 when x = 8

Explanation:

If y varies inversely as the cube root of x then we can express this algebraically thus

`y = k*1/x^(1/3)`

Using the values `y = 4` when `x = 27`

We get `4 = k / 27^(1/3 )`
`4 = k /3`

Therefore `k = 12`

The relationship can now be fully expressed as `y = 12/x^(1/3 )`

Using this rule when `x = 8`

`y = 12 / 8^(1/3) = 12/2 = 6`