JAMB - Mathematics (1997 - No. 12)
Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)
\(\frac{gv-t^2}{gt^2}\)
\(\frac{gt^2}{gv-t^2}\)
\(\frac{v}{\frac{1}{t^2} - \frac{1}{g}}\)
\(\frac{gv}{t^2 - g}\)
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 = \(\frac{gt^2}{gv-t^2}\)
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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