(a) By how much is the sum of \(3\frac{2}{3}\) and \(2\frac{1}{5}\) less than 7? (b) The height, h m, of a dock above sea level is given by \(h = 6 + 4\cos ...
Question 1 Report
(a) By how much is the sum of \(3\frac{2}{3}\) and \(2\frac{1}{5}\) less than 7?
(b) The height, h m, of a dock above sea level is given by \(h = 6 + 4\cos (15p)°, 0 < p < 6\). Find :
(i) the value of h when p = 4 ; (ii) correct to two significant figures, the value of p when h = 9 m.
Answer Details
(a) Sum \(= 3\tfrac{2}{3} + 2\tfrac{1}{5} = \tfrac{11}{3} + \tfrac{11}{5} = \tfrac{55 + 33}{15} = \tfrac{88}{15}\).
It is less than 7 by \(7 - \tfrac{88}{15} = \tfrac{105 - 88}{15} = \tfrac{17}{15} = 1\tfrac{2}{15}\).
(b)(i) With \(p = 4\): \(15p = 60^{\circ}\) and \(\cos 60^{\circ} = 0.5\).
\[h = 6 + 4(0.5) = 8 \text{ m}\](b)(ii) With \(h = 9\):
\[9 = 6 + 4\cos(15p)^{\circ} \Rightarrow \cos(15p)^{\circ} = 0.75\] \[15p = \cos^{-1} 0.75 = 41.4^{\circ} \Rightarrow p = \frac{41.4}{15} = 2.8 \text{ (2 s.f.)}\]Download The App On Google Playstore
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