Chapter 8.1, Problem 25WE

To determine

To show that $yz$ varies directly as $y^2+z^2$ .

Explanation of Solution

Given information:

The given statement is:

“The numbers $x,y\text{ and }z$ are positive numbers such that $y$ varies directly as $x$ , and $z$ varies directly as $x$ .”

Proof:

Since, $y\text{ and }z$ varies directly with $x$ so the product of $y\text{ and }z$ and the sum of squares of $y\text{ and }z$ will also vary directly with $x$ .

Hence, $yz$ varies directly as $y^2+z^2$ .