If w varies inversely as uv/u+v and w = 8 when u = 2 and v = 6, find a relationship between u, v, w.

Correct Answer is : uvw = 12(u + v)

Correct Answer is : uvw = 12(u + v)

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JAMB Mathematics 2021 Paper

Question : 29

Total: 40

\frac{uv}{u+v}

u = 2 and v = 6, find a relationship between u, v, w.

Solution:

Concept:

Inverse variation means that if

w

varies inversely as

\frac{uv}{u+v}

, then

w = k \times \frac{u+v}{uv}

Explanation:

Start with the inverse variation relationship:

w = \frac{k(u+v)}{uv}

Substitute

w = 8

u = 2

, and

v = 6

8 = \frac{k(2+6)}{2 \times 6}

This gives:

8 = \frac{8k}{12}

Simplify:

8 = \frac{2k}{3}

Multiply both sides by

3

24 = 2k

k = 12

Now write the relationship:

w = \frac{12(u+v)}{uv}

Multiply both sides by

uv

uvw = 12(u+v)

Answer:

uvw = 12(u+v)

, so the correct option is C.

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