Chapter 12.8, Problem 5OE

To determine

To Describe: The statement into a formula,

  $Y$ varies directly as the square of $X^2$ and inversely as square of $Z^2$ .

Answer to Problem 5OE

The formula of the statement is $Y=K\frac{X^2}{Z^2}$ .

Explanation of Solution

Given information:

Translate statement to formula:

  $Y$ varies directly as the square of $X^2$ and inversely as square of $Z^2$ .

Use $K$ as constant.

Consider the statement,

  $Y$ varies directly as the square of $X^2$ and inversely as square of $Z^2$ .

Here if a variable varies directly as he product of two or more other variables the resulting relationship is a joint variation.

As $Y$ is directly as square of $X^2$ ,

  $Y\alpha X^2$ .

Then $Y$ is inversely as square of $Z^2$ .

  $Y\alpha \frac{1}{Z^2}$

From both equations:

  $\begin{array}{c}Y\alpha X^2\\ Y\alpha \frac{1}{Z^2}\\ Y\alpha \frac{X^2}{T^2}\end{array}$

Same as above,

Here,

  $Y\alpha \frac{X^2}{T^2}$

For replacing $\alpha$ apply constant $K$ .

  $\begin{array}{l}Y\alpha \frac{X^2}{T^2}\\ Y=K\frac{X^2}{T^2}\end{array}$

Thus, the formula is: $Y=K\frac{X^2}{T^2}$ .