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.
Answer Details
We are given that "M varies directly as n and inversely as the square of p." This means that M is directly proportional to n and inversely proportional to the square of p. We can represent this relationship mathematically as:
M ∝ n/p^2
where the symbol ∝ means "is proportional to".
We are also given that M = 3 when n = 2 and p = 1. We can use this information to find the constant of proportionality k:
M ∝ n/p^2
3 ∝ 2/1^2
3 ∝ 2
To find k, we can write:
M = k(n/p^2)
Substituting the values we know:
3 = k(2/1^2)
k = 3/2
Now we can use k to find M in terms of n and p:
M = (3/2)(n/p^2)
Simplifying, we get:
M = (3n)/(2p^2)
Therefore, the answer is option D: M = 3n/2p^2.