# How do you write a general formula to describe each variation if the cube of z varies directly with the sum of the squares of x and y; z=2 when x=9 and y=4?

Feb 22, 2017

${z}^{3} = \frac{8}{97} \left({x}^{2} + {y}^{2}\right)$

#### Explanation:

As ${z}^{3}$ varies directly with the sum of the squares of $x$ and $y$ i.e. ${x}^{2} + {y}^{2}$, we can say

${z}^{3} = k \times \left({x}^{2} + {y}^{2}\right)$

Now, as when $x = 9$ and $y = 4$, we have $z = 2$

${2}^{3} = k \times \left({9}^{2} + {4}^{2}\right) = k \times \left(81 + 16\right) = 97 k$

i.e. $k = \frac{8}{97}$

Hence ${z}^{3} = \frac{8}{97} \left({x}^{2} + {y}^{2}\right)$