M varies jointly as the square of n and square root of q. If M...
MATHEMATICS
WAEC 2023
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: D. 225
Explanation
\(M ∝ n^2\sqrt{q}\)
\(M = Kn^2\sqrt{q}\)
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.
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