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

The problem tells us that M varies directly as n and inversely as the square of p. This can be written as: M ∝ n/p^2 Where the symbol "∝" means "is proportional to". We can also write this using a constant of proportionality k: M = k(n/p^2) To find the value of k, we can use the values of M, n, and p given in the problem: 3 = k(2/1^2) Simplifying this equation, we get: k = 3/2 Now we can use this value of k to find M in terms of n and p: M = (3/2)(n/p^2) Simplifying further: M = (3n)/(2p^2) Therefore, the answer is: - 3n/(2p^2)