Question

Write an equation that expresses the statement.

A is jointly proportional to the square roots of x and y.

Short answer

Equation that represents the statement is $\mathrm{A}=\mathrm{k}\left(\sqrt{\mathrm{xy}}\right)$.

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. Write the equation.

The relation between variables is proportional hence,

$\mathrm{A}=\mathrm{k}\left(\sqrt{\mathrm{x}}\times \sqrt{\mathrm{y}}\right)$

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

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

Equation is:

$\mathrm{A}=\mathrm{k}\left(\sqrt{\mathrm{xy}}\right)$