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Worked Solutions for 2003/2004 S1 Semestral Exam

NO

SOLUTION

1 2 3 4 5

D D B B A

6a (i)

log x  log(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)sin 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 Rate of receipts is falling because more people have seen the show. When t = 1,
8(a)

3x  4y  2x 3 y Differentiate both 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 labour increases from 4 to 6 units, P=120  2=240 Therefore 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 Therefore 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 cost is minimised. At p =24,

NO

SOLUTION

9(b) Pr ofit  Re venue  Cost (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...

• Submitted by: neumannchew
• on October 5, 2012
• Length: 680 words
• Views: 300
• Popularity Rank: 387069
• 1 rating(s)

### Citations

##### MLA Citation

"Business Math". Anti Essays. 9 Dec. 2018