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

May 17, 2017

y = 6 when x = 8

#### Explanation:

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

$y = k \cdot \frac{1}{x} ^ \left(\frac{1}{3}\right)$

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

We get $4 = \frac{k}{27} ^ \left(\frac{1}{3}\right)$
$4 = \frac{k}{3}$

Therefore $k = 12$

The relationship can now be fully expressed as $y = \frac{12}{x} ^ \left(\frac{1}{3}\right)$

Using this rule when $x = 8$

$y = \frac{12}{8} ^ \left(\frac{1}{3}\right) = \frac{12}{2} = 6$