If p varies inversely as the square of q and p = 8 when q = 4, find q when p = 32
A
\(\pm\)16
B
\(\pm\)8
C
\(\pm\)4
D
\(\pm\)2
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
p ∝ \(\frac{1}{q}\)
p = \(\frac{k}{q}\)
K = q\(^2\)p
= 4\(^2\)(8)
∴ p = \(\frac{128}{\text{q}}\)
32 = \(\frac{128}{\text{q}}\)
q\(^2\) = \(\frac{128}{32}\)
q\(^2\) = 4
q = \sqrt4 = \(\pm\) 2
Source: Myschool Past Questions Archive (Record #9272)