Question

1. if ( q ) is inversely proportional to ( r ) squared and ( q = 30 ) when ( r = 3 ), find ( r ) when ( q = 1.2 ).

Explanation:

Step1: Write inverse proportion formula

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

Step2: Solve for constant $k$

Substitute $q=30$, $r=3$:
$30 = \frac{k}{3^2} \implies 30 = \frac{k}{9} \implies k = 30 \times 9 = 270$

Step3: Substitute $k$ and new $q$

Use $k=270$, $q=1.2$:
$1.2 = \frac{270}{r^2}$

Step4: Solve for $r^2$

Rearrange to isolate $r^2$:
$r^2 = \frac{270}{1.2} = 225$

Step5: Solve for positive $r$

Take square root of both sides:
$r = \sqrt{225} = 15$

Answer:

$r = 15$