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


Question

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

Options

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

B) \(\frac{1}{3}\)

C) 3

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

The correct answer is D.

Explanation:

If P = \(\frac{2}{3}\) (\(\frac{1 - r^2}{n^2}\)), find n when r = \(\frac{1}{3}\) and p = 1
p = \(\frac{2(1 - r^2)}{3n^2}\) when r = \(\frac{1}{3}\) and p = 1
1 = \(\frac{2}{3}\) \(\frac{(1 - (\frac{1}{3})^2)}{n^2}\)
n2 = \(\frac{2(3 - 1)}{3 \times 3}\)
n2 = \(\frac{2 \times 2}{3 \times 3}\)
= \(\frac{4}{9}\)
n = \(\frac{4}{9}\)
= \(\frac{2}{3}\)

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Dicussion (1)

  • If P = \(\frac{2}{3}\) (\(\frac{1 - r^2}{n^2}\)), find n when r = \(\frac{1}{3}\) and p = 1
    p = \(\frac{2(1 - r^2)}{3n^2}\) when r = \(\frac{1}{3}\) and p = 1
    1 = \(\frac{2}{3}\) \(\frac{(1 - (\frac{1}{3})^2)}{n^2}\)
    n2 = \(\frac{2(3 - 1)}{3 \times 3}\)
    n2 = \(\frac{2 \times 2}{3 \times 3}\)
    = \(\frac{4}{9}\)
    n = \(\frac{4}{9}\)
    = \(\frac{2}{3}\)

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