T varies inversely as the cube of R. When R = 3, T = \(\frac{2}{81}\),...

Mathematics

JAMB 2011

T varies inversely as the cube of R. When R = 3, T = \(\frac{2}{81}\), find T when R = 2

A. \(\frac{1}{18}\)
B. \(\frac{1}{12}\)
C. \(\frac{1}{24}\)
D. \(\frac{1}{6}\)

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Correct Answer: Option B

Explanation

T \(\alpha \frac{1}{R^3}\)

T = \(\frac{k}{R^3}\)

k = TR³

= \(\frac{2}{81}\) x 3³

= \(\frac{2}{81}\) x 27

dividing 81 by 27

k = \(\frac{2}{2}\)

therefore, T = \(\frac{2}{3}\) x \(\frac{1}{R^3}\)

When R = 2

T = \(\frac{2}{3}\) x \(\frac{1}{2^3}\) = \(\frac{2}{3}\) x \(\frac{1}{8}\)

= \(\frac{1}{12}\)

There is an explanation video available below.

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