Question

select the correct answer from each drop-down menu. the variable p varies inversely as the square of q. when p = 36, q = 25. when p = 4, q = . when q = 10, p = .

Explanation:

Step1: Define inverse variation formula

$p = \frac{k}{q^2}$, where $k$ is the constant of variation.

Step2: Solve for constant $k$

Substitute $p=36$, $q=25$:
$36 = \frac{k}{25^2}$
$k = 36 \times 625 = 22500$

Step3: Find $q$ when $p=4$

Substitute $p=4$, $k=22500$:
$4 = \frac{22500}{q^2}$
$q^2 = \frac{22500}{4} = 5625$
$q = \sqrt{5625} = 75$

Step4: Find $p$ when $q=10$

Substitute $q=10$, $k=22500$:
$p = \frac{22500}{10^2} = \frac{22500}{100} = 225$

Answer:

When $p = 4$, $q = 75$
When $q = 10$, $p = 225$