JAMB 1987 · UME · Q16

Expressions, formulae & change of subject

If $p = \dfrac{2}{3} \cdot \dfrac{1 - r^2}{n^2}$ , find $n$ when $r = \frac{1}{\sqrt3}$ and $p = 1$ .

Worked solution (try it first)

With $r = \frac{1}{\sqrt3}$ , $r^2 = \frac13$ , so $1 - r^2 = \frac23$ .
Substitute: $1 = \frac23 \times \frac{2/3}{n^2}$
$= \frac{4}{9n^2}$ .
Multiply by $9n^2$ : $9n^2 = 4$ , so $n^2 = \frac49$ .
Take the square root: $n = \frac23$ , option D.

Report a problem with this question