(a) Simplify : \(\frac{3\frac{1}{12} + \frac{7}{8}}{2\frac{1}{4} – \frac{1}{6}}\)
(b) If \(p = \frac{m}{2} – \frac{n^{2}}{5m}\) ;
(i) make n the subject of the relation ; (ii) find, correct to three significant figures, the value of n when p = 14 and m = -8.
Explanation
(a) \(\frac{3\frac{1}{12} + \frac{7}{8}}{2\frac{1}{4} - \frac{1}{6}}\)
\(3\frac{1}{12} + \frac{7}{8} = \frac{37}{12} + \frac{7}{8}\)
= \(\frac{74 + 21}{24}\)
= \(\frac{95}{24}\)
\(2\frac{1}{4} - \frac{1}{6} = \frac{9}{4} - \frac{1}{6}\)
= \(\frac{27 - 2}{12}\)
= \(\frac{25}{12}\)
\(\therefore \frac{3\frac{1}{12} + \frac{7}{8}}{2\frac{1}{4} - \frac{1}{6}} = \frac{95}{24} \div \frac{25}{12}\)
\(\frac{95}{24} \times \frac{12}{25} = \frac{19}{10}\)
= \(1.9\)
(b)(i) \(p = \frac{m}{2} - \frac{n^{2}}{5m}\)
\(\frac{n^{2}}{5m} = \frac{m}{2} - p\)
\(n^{2} = 5m(\frac{m}{2} - p)\)
\(n = \pm \sqrt{5m(\frac{m}{2} - p)}\)
(ii) When p = 14 and m = -8,
\(n = \sqrt{5(-8)(\frac{-8}{2} - 14)}\)
\(n = \sqrt{-40(- 4 - 14)}\)
\(n = \sqrt{720}\)
\(n = 12\sqrt{5}\)
= \(\pm 26.83\)