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JAMB Mathematics 2012 Paper

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Question : 14

Total: 48

U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

24
27
32
36

Solution:

Concept:

Inverse proportion means

U = \frac{k}{V^3}

; find

k

first, then solve for the new

U

.

Explanation:

Since

U

is inversely proportional to

V^3

, write

U \propto \frac{1}{V^3}

.

So

U = \frac{k}{V^3}

, where

k

is a constant.

Given

U = 81

when

V = 2

:

81 = \frac{k}{2^3}

k = 81 \times 8

Now find

U

when

V = 3

:

U = \frac{81 \times 8}{3^3}

U = \frac{648}{27} = 24

Answer:

U = 24

, so the correct option is A.

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