Business Math

Worked Solutions for 2003/2004 S1 Semestral Exam NO SOLUTION 1 2 3 4 5 D D B B A 6a (i) put down x ? recordarithmarithm(x ? 1) ? ?1 x log ? ?1 x ?1 x 1 ? x ? 1 10 10x ? x ? 1 1 x? 9 5x ? 32x ?1 log 5x ? log 32x ?1 x log 5 ? (2x ? 1) log 3 x log 5 ? 2x log 3 ? log 3 x(log 5 ? 2 log 3) ? log 3 log 3 x? ? ?1.87 log 5 ? 2 log 3 (ii) NO SOLUTION 6(b) (i) 1 2 ? x ? 9 ? ? 50 3 When x = 0 1 2 S(0) ? ? ? 0 ? 9 ? ? 50 ? $23, 000 3 S(x) ? ? (ii) When x = 15 1 S(15)=- (15 ? 9)2 ? 50 ? $38, 000 3 (iii) 7(a) (i) (ii) NO SOLUTION 7(a) (i) y ? 5x ? 2x ? 6 dy ? 15x 2 ? 4x ?3 dx 3 ?2 (ii) y ? (3x 2 ? 1) ungodliness 2x dy ? (3x 2 ? 1)2 cos 2x ? sin 2x(6x) ? 2 ? 3x 2 ? 1 cos 2x ? 3x sin 2x ? ? ? dx ? ? 7(b) B? 80t 2 t2 ? 3 2 2 dB ? t ? 3? ?160t ? ? 80t ? 2t ? 480t ? ? 2 2 dt ? t 2 ? 3? ? t 2 ? 3? dB 480 ? 2 ? 30million dt 4 dB 480(3) When t = 3, ? ? 10million dt 122 tar contract of receipts is falling because much large number swallow seen the show.

When t = 1, 8(a) 3x ? 4y ? 2x 3 y Differentiate both(prenominal) sides wrt x 3 3x dy dy ? 2 ?4 ? 6x 2 y y dx dx dy ? 3x ? 3 2 ? 4 ? 2 ? ? 6x ? dx ? y ? y 3 dy y ? dx 4 ? 3x y2 6x 2 ? NO SOLUTION 8(b) (i) P(x, y) ? 150 x 2 ? y 2 ?P 150x ? ?x x 2 ? y2 ?P 150y ? ?y x 2 ? y2 When x = 4 and y = 3 ? P 150(4) ? ? 120 ?x 42 ? 32 ? P 150(3) ? ? 90 ?y 42 ? 32 If roil increases from 4 to 6 units, ?P=120 ? 2=240 then production increases by 240 units. If capital decreases from 3 to 2 units and labour decreases from 4 to 3 units, ?P=120 ? -1+90 ? -1=-210 accordingly production reduces by 210 units. (ii) 9(a) Average cos t ? 2p ? 375 ? dAC 1152 ? 2? 2 dp p 1152 2? 2 ? 0 p p ? 24 d 2 AC 2304 ? 3 dp 2 p 1152 p d 2 AC 2304 ? ?0 dp 2 243 Therefore at p = 24, average follow is minimised. At p =24, NO SOLUTION 9(b) Pr ofit ? Re venue ? speak to (i) Pr ofit ? 156x ? 0.7x 2 ? 4575 ? 0.3x 2 ? 156x ? x 2 ? 4575 (ii) To get max profit, dprofit ?0 dx 156 ? 2x ? 0 x ? 78 d 2...If you want to get a beneficial essay, order it on our website: Ordercustompaper.com

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