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If w varies inversely as V and U varies directly as w3, Find the relationship...

Mathematics
JAMB 1983

If w varies inversely as V and U varies directly as w3, Find the relationship between u and v given that u = 1, when v = 2
  • A. u = \(\frac{8}{v^3}\)
  • B. v = \(\frac{8}{u^2v^3}\)
  • C. u = 8v3
  • D. v = 8u2
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Correct Answer: Option A
Explanation
W \(\alpha\) \(\frac{1}{v}\)u \(\alpha\) w3

w = \(\frac{k1}{v}\)

u = k2w3

u = k2(\(\frac{k1}{v}\))3

= \(\frac{k_2k_1^2}{v^3}\)

k = k2k1k2

u = \(\frac{k}{v^3}\)

k = uv3

= (1)(2)3

= 8

u = \(\frac{8}{v^3}\)

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