(a) Simplify : (frac{3frac{1}{12} + frac{7}{8}}{2frac{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{3frac{1}{12} + frac{7}{8}}{2frac{1}{4} – frac{1}{6}})
(3frac{1}{12} + frac{7}{8} = frac{37}{12} + frac{7}{8})
= (frac{74 + 21}{24})
= (frac{95}{24})
(2frac{1}{4} – frac{1}{6} = frac{9}{4} – frac{1}{6})
= (frac{27 – 2}{12})
= (frac{25}{12})
(therefore frac{3frac{1}{12} + frac{7}{8}}{2frac{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 = 12sqrt{5})
= (pm 26.83)