Question

Write an equation that expresses the statement.

S is proportional to the product of the squares of r and $\mathrm{\theta }$.

Short answer

Equation that represents the statement is$\mathrm{S}=\mathrm{k}{\left(\mathrm{r\theta }\right)}^2$.

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. Write the equation.

The relation between variables is proportional hence,

$\mathrm{S}=\mathrm{k}\left({\mathrm{r}}^2\times {\mathrm{\theta }}^2\right)$

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

Step 3. Write the final equation representing the given statement.

Equation is:

$\mathrm{S}=\mathrm{k}{\left(\mathrm{r\theta }\right)}^2$