Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)

Mathematics

JAMB 1997

A. \(\frac{gv-t^2}{gt^2}\)
B. \(\frac{gt^2}{gv-t^2}\)
C. \(\frac{v}{\frac{1}{t^2} - \frac{1}{g}}\)
D. \(\frac{gv}{t^2 - g}\)

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Correct Answer: Option B

Explanation

t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)

t² = \(\frac{v}{\frac{1}{f} + \frac{1}{g}}\)

= \(\frac{vfg}{ftg}\)

\(\frac{1}{f} + \frac{1}{g}\) = \(\frac{v}{t^2}\)

= (g + f)t² = vfg

gt² = vfg - ft²

gt² = f(vg - t²)

f = \(\frac{gt^2}{gv-t^2}\)

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