# 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?

May 29, 2018

$y = 31 \frac{1}{2}$

#### Explanation:

For y to vary directly with x and inversely with the square of z, we can write $y = k \frac{x}{z} ^ 2$

We are told that $6 = k \cdot \frac{64}{8} ^ 2 = k$ i.e. $k = 6$

Therefore $y = 6 \frac{x}{z} ^ 2$
When $x = 21 , z = 2$ this gives us $y = 6 \cdot \frac{21}{2} ^ 2 = \frac{63}{2} = 31 \frac{1}{2}$

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