Chapter 12.8, Problem 3OE

To determine

To Describe: The statement into a formula,

  $a$ varies directly as the square of $b$ and inversely as $c$ .

Answer to Problem 3OE

The formula of the statement is $a=k\frac{b^2}{c}$ .

Explanation of Solution

Given information:

Translate statement to formula:

  $a$ varies directly as the square of $b$ and inversely as $c$ .

Use $K$ as constant.

Consider the statement,

  $a$ varies directly as the square of $b$ and inversely as $c$ .

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

As $a$ is directly as square of $b$ ,

  $a\alpha b^2$ .

Then $a$ is inversely as $c$ .

  $a\alpha \frac{1}{c}$

From both equations:

  $\begin{array}{c}a\alpha b^2\\ a\alpha \frac{1}{c}\\ a\alpha \frac{b^2}{c}\end{array}$

Same as above,

Here,

  $a\alpha \frac{b^2}{c}$

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

  $\begin{array}{l}a\alpha \frac{b^2}{c}\\ a=k\frac{b^2}{c}\end{array}$

Thus, the formula is: $a=k\frac{b^2}{c}$ .