Express: z varies directly with the sum of the squares of x and y.

We will use the concept of direct and inverse proportion to find the answer.

Answer : z = k ( x² + y² ), where k is a constant of proportionality.

Let us see how we will use the concept of direct and inverse proportion to find the answer.

Explanation:

Let us first write the expression of the sum of squares of x and y which is equal to x² + y².

Now, z varies with direct proportion with the sum of squares of x and y.

So, it can be written mathematically as  z ∝ ( x² + y² ) 

When we remove a sign of proportionality then a constant comes which is called the constant of proportionality. So, z = k ( x² + y² ), where k is a constant of proportionality.

Hence, the final expression can be written as z = k ( x² + y² ), where k is a constant of proportionality.