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WAEC Mathematics 2023 Paper

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Question : 49

Total: 50

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.

288
400
300
225

Solution:

Concept:

Joint variation combines two relationships into one equation using a constant

k

.

Explanation:

Since

M

varies jointly as

n^2

and

\sqrt{q}

, write

M = k n^2 \sqrt{q}

.

Substitute

M = 24

,

n = 2

,

q = 4

:

24 = k(2^2)(\sqrt{4}) = k(4)(2) = 8k

.

So

k = \frac{24}{8} = 3

.

Now substitute

k = 3

,

n = 5

,

q = 9

:

M = 3(5^2)(\sqrt{9}) = 3(25)(3) = 225

.

Answer:

M = 225

, which is option D.

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