(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 ...
Question 1 Report
(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.
Answer Details
(a) Numerator: \(3\tfrac{1}{12} + \tfrac{7}{8} = \tfrac{37}{12} + \tfrac{7}{8} = \tfrac{74}{24} + \tfrac{21}{24} = \tfrac{95}{24}.\)
Denominator: \(2\tfrac{1}{4} - \tfrac{1}{6} = \tfrac{9}{4} - \tfrac{1}{6} = \tfrac{27}{12} - \tfrac{2}{12} = \tfrac{25}{12}.\)
\[\frac{95/24}{25/12} = \frac{95}{24}\times\frac{12}{25} = \frac{95}{2\times 25} = \frac{95}{50} = \frac{19}{10} = \mathbf{1\tfrac{9}{10}}.\]
(b)(i) \(p = \dfrac{m}{2} - \dfrac{n^2}{5m}.\) Multiply through by \(5m\): \[5mp = \frac{5m^2}{2} - n^2 \Rightarrow n^2 = \frac{5m^2}{2} - 5mp \Rightarrow \mathbf{n = \sqrt{\frac{5m^2}{2} - 5mp}}.\]
(b)(ii) With \(p = 14,\ m = -8\): \[n^2 = \frac{5(-8)^2}{2} - 5(-8)(14) = \frac{320}{2} + 560 = 160 + 560 = 720.\] \[n = \sqrt{720} = \mathbf{26.8}\ (\text{to 3 s.f.}).\]
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