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JAMB Mathematics 2014 Paper

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Question : 13

Total: 47

y varies directly as w². When y = 8, w = 2. Find y when w = 3

18
12
9
6

Solution:

Concept:

Direct variation with a square means

y

is equal to a constant

k

multiplied by

w^{2}

.

Explanation:

Since

y

varies directly as

w^{2}

, write

y = k w^{2}

.

Use

y = 8

and

w = 2

to find

k

.

Substitute:

8 = k(2^{2})

.

This gives

8 = 4k

.

So

k = \frac{8}{4} = 2

.

The equation becomes

y = 2w^{2}

.

Now find

y

when

w = 3

.

Substitute:

y = 2(3^{2}) = 2 \times 9

.

Therefore,

y = 18

.

Answer:

y = 18

(Option A).

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