# How do you write a general formula to describe each variation if z varies directly with the sum of the cube of x and the square of y; z=1 when x=2 and y=3?

Oct 8, 2016

General formula is $z = \frac{1}{17} \left({x}^{3} + {y}^{2}\right)$

#### Explanation:

When a variable say $z$ varies directly with say $w$

we have $z \propto w$ i.e. $z = w \times k$, where $k$ is a constant.

Here $w$ is the sum of the cube of $x$ and the square of $y$

Hence $z = \left({x}^{3} + {y}^{2}\right) \times k$ ......................(1)

When $z = 1$ when $x = 2$ and $y = 3$, (1) becomes

$1 = \left({2}^{3} + {3}^{2}\right) \times k$

or $1 = \left(8 + 9\right) \times k$

or $17 k = 1$ i.e. $k = \frac{1}{17}$

Hence, general formula is $z = \frac{1}{17} \left({x}^{3} + {y}^{2}\right)$