Theory question 106
Algebraic Expressions(a) Simplify (x2/2 − x + 1/2)(1/(x − 1))
(b) A point P is 40 km from Q on a bearing 061°. Calculate, correct to one decimal place, the distance of P to (i) north of Q; (ii) east of Q.
(c) A man left N5,720 to be shared among his son and three daughters. Each daughter's share was ¾ of the son's share. How much did the son receive?
Show the model answer
Model answer
(a) x2/2 − x + 1/2 = (x2 − 2x + 1)/2 = (x − 1)2/2. Multiply by 1/(x − 1): (x − 1)/2.
(b)(i) North: 40 cos 61° = 40 × 0.4848 ≈ 19.4 km.
(ii) East: 40 sin 61° = 40 × 0.8746 ≈ 35.0 km.
(c) Son s, each daughter ¾s: s + 3 × ¾s = 13s/4 = 5720, so s = N1,760.
Explanation
The bearing is measured from north, so north uses cosine and east uses sine.