Theory question 102
Algebraic Expressions(a) Given that P = (rk/Q − ms)2/3, (i) make Q the subject of the relation; (ii) find, correct to two decimal places, the value of Q when P = 3, m = 15, s = 0.2, k = 4 and r = 10.
(b) Given that (x + 2y)/5 = x − 2y, find x : y.
Show the model answer
Model answer
(a)(i) Raise both sides to the power 3/2: P3/2 = rk/Q − ms
rk/Q = P3/2 + ms → Q = rk/(P3/2 + ms)
(ii) Q = 40/(33/2 + 3) = 40/(5.196 + 3) = 40/8.196 ≈ 4.88
(b) x + 2y = 5x − 10y → 12y = 4x
x/y = 3, so x : y = 3 : 1
Explanation
Undo the power 2/3 by raising both sides to 3/2.