M varies directly with the square of n and inversely with p. When n= 2 and p=6,m=9, find m when n=4 and p=8
First, we can write the relationship as an equation:
m = k * (n^2) / p
Where k is the constant of proportionality. We can find k using the initial values given when n=2 and p=6:
9 = k * (2^2) / 6
9 = k * 4 / 6
9 = 4k / 6
54 = 4k
k = 13.5
Now that we have k, we can find m when n=4 and p=8:
m = 13.5 * (4^2) / 8
m = 13.5 * 16 / 8
m = 216 / 8
m = 27
Therefore, when n=4 and p=8, m=27.