Question

Write an equation that expresses the statement.

R is proportional to the product of the squares of P and t and inversely proportional to the cube of b.

Short answer

Equation that represents the statement is $\mathrm{R}=\mathrm{k}\left(\frac{{\mathrm{P}}^2\times {\mathrm{t}}^2}{{\mathrm{b}}^3}\right)$.

Step-by-step solution

Step 1. Understanding Direct variation.

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

For example:

$\mathrm{y}=\mathrm{kx}$

Here $\mathrm{k}\ne 0$, y is directly proportional to x and vice versa.

Step 2. Understanding inverse proportion.

The relation between two variables is inversely proportional when,

$\mathrm{y}=\frac{\mathrm{k}}{\mathrm{x}}$or $\mathrm{xy}=\mathrm{k}$

Here $\mathrm{k}\ne 0$, y is inversely proportional to x and vice versa.

Step 3. Write the equation that expresses the statement.

Equation is:

$\mathrm{R}=\mathrm{k}\left(\frac{{\mathrm{P}}^2\times {\mathrm{t}}^2}{{\mathrm{b}}^3}\right)$

Where k is any constant and k is not equal to zero.