Question

question 5 of 5
select the correct answer.
the square of z varies inversely as the square root of w. if z = 36 when w = 16, what is the value of z when w = 81?
○ $7\frac{1}{9}$
○ $182\frac{1}{4}$
○ 54
○ 24

Explanation:

Step1: Define inverse variation relation

$z^2 = \frac{k}{\sqrt{w}}$, where $k$ is constant.

Step2: Solve for constant $k$

Substitute $z=36$, $w=16$:
$36^2 = \frac{k}{\sqrt{16}}$
$1296 = \frac{k}{4}$
$k = 1296 \times 4 = 5184$

Step3: Find $z$ when $w=81$

Substitute $k=5184$, $w=81$:
$z^2 = \frac{5184}{\sqrt{81}} = \frac{5184}{9} = 576$
$z = \sqrt{576} = 24$

Answer:

24