Theory question 104
Fractions, Decimals and Approximation(a) By how much is the sum of 3⅔ and 2⅕ less than 7?
(b) The height, h m, of a dock above sea level is given by h = 6 + 4cos(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 = 9m.
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Model answer
(a) 3⅔ + 2⅕ = 55/15 + 33/15 = 88/15 = 513/15
7 − 513/15 = 12/15
(b)(i) h = 6 + 4cos 60° = 6 + 4 × 0.5 = 8 m
(ii) 9 = 6 + 4cos(15p)° → cos(15p)° = 0.75 → 15p = 41.41° → p = 2.76 ≈ 2.8
Explanation
In (b)(ii), make cos(15p)° the subject before using inverse cosine.