If P = \(\frac{\frac{2}{3}({1 - r^2})}{n^2}\), find n when r = \(\sqrt{\frac{1}{3}}\) and p =...

Mathematics

JAMB 1987

If P = \(\frac{\frac{2}{3}({1 - r^2})}{n^2}\), find n when r = \(\sqrt{\frac{1}{3}}\) and p = 1

A. \(\frac{3}{2}\)
B. \(\frac{1}{3}\)
C. 3
D. \(\frac{2}{3}\)

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Correct Answer: Option D

Explanation

If P = \(\frac{\frac{2}{3}({1 - r^2})}{n^2}\), find n when r = \(\sqrt{\frac{1}{3}}\) and p = 1

p = \(\frac{\frac{2}{3}({1 - r^2})}{n^2}\) when r = \(\sqrt{\frac{1}{3}}\) and p = 1

1 = \(\frac{\frac{2}{3}({1 - (\sqrt{\frac{1}{3}})^2})}{n^2}\)

\(n^2\) = \(\frac{2}{3}(1 - \frac{1}{3}\))

\(n^2\) = \(\frac{2 \times 2}{3 \times 3}\)

= \(\frac{4}{9}\)

n = \(\sqrt{\frac{4}{9}}\)

= \(\frac{2}{3}\)