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)