M varies jointly as the square of n and square root of q. If M = 24 when n = 2 and q = 4, find M when n = 5, q = 9.
A.
288
B.
400
C.
300
D.
225
Correct answer is D
\(M ∝ n^2\sqrt{q}\)
\(M = Kn^2\sqrt{q}\)
K = \(\frac{M}{n^2\sqrt{q}}\)
K = \(\frac{24}{2^2\sqrt4}\)
k = \(\frac{24}{8} = 3\)
Now, let's find M when n = 5 and q = 9
M = \(Kn^2\sqrt{q}\)
M = \( 3\times5^2\sqrt9\)
\(M = 3\times25\times3\)
Therefore, M = 225.
