M varies directly as n and inversely as the square of p. If M = 3, when n = 2 and p = 1, find M in terms of n and p.
A
M = 2n/3p
B
M = 3n2/2p2
C
M = n2/2p
D
M = 3n/2p2
E
M = 2n/3p2
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(M \propto \frac{n}{p^2}\)
\(M = \frac{kn}{p^2}\)
\(3 = \frac{k(2)}{1^2}\)
\(3 = 2k \implies k = \frac{3}{2}\)
\(M = \frac{3n}{2p^2}\)
Source: Myschool Past Questions Archive (Record #23801)