Question

Write a general formula to

describe the variation
Z varies directly with the
Sum of the Squares of Xandy
Z=2 when X=4 and y = 5
Z=

Answer 1

`\\\\z = (2)/(41)(x^2 + y^2)`

Explanation:

We have

`z \propto x^2 + y^2\\\\`

This can be expressed as an equation:

`z = k \cdot (x^2 + y^2)\\\\`

where k is known as the constant of proportionality

To find k

substitute given values z = 2 , x = 4 , y = 5

`2 = k(4^2 + 5^2)\\\\2 = k (16 + 25)\\\\2 = k\cdot 41\\\\\\\longrightarrow k = (2)/(41)\\\\`

So the equation is

`\\\\z = (2)/(41)(x^2 + y^2)`