Chapter 12.8, Problem 4OE

To determine

To Describe: The statement into a formula,

  $Q$ varies directly as $M$ and inversely as square of $T^2$ .

Answer to Problem 4OE

The formula of the statement is $Q=K\frac{M}{T^2}$ .

Explanation of Solution

Given information:

Translate statement to formula:

  $Q$ varies directly as $M$ and inversely as square of $T^2$ .

Use $K$ as constant.

Consider the statement,

  $Q$ varies directly as $M$ and inversely as square of $T^2$ .

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

As $Q$ is directly as $M$ ,

  $Q\alpha M$ .

Then $Q$ is inversely as square of $T$ .

  $Q\alpha \frac{1}{T^2}$

From both equations:

  $\begin{array}{c}Q\alpha M\\ Q\alpha \frac{1}{T^2}\\ Q\alpha \frac{M}{T^2}\end{array}$

Same as above,

Here,

  $Q\alpha \frac{M}{T^2}$

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

  $\begin{array}{l}Q\alpha \frac{M}{T^2}\\ Q=K\frac{M}{T^2}\end{array}$

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