JAMB - Mathematics (1987 - No. 14)
If P = \(\frac{\frac{2}{3}({1 - r^2})}{n^2}\), find n when r = \(\sqrt{\frac{1}{3}}\) and p = 1
\(\frac{3}{2}\)
\(\frac{1}{3}\)
3
\(\frac{2}{3}\)
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 = \(\sqrt{\frac{4}{9}}\)
= \(\frac{2}{3}\)
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 = \(\sqrt{\frac{4}{9}}\)
= \(\frac{2}{3}\)
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