Question

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?

Answer 1

`z^3=8/97(x^2+y^2)`

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=kxx(x^2+y^2)`

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

`2^3=kxx(9^2+4^2)=kxx(81+16)=97k`

i.e. `k=8/97`

Hence `z^3=8/97(x^2+y^2)`