basic_engineering_mathematics0

Answers to exercises 273
7. ab 6 c 3/2 8. a −4 b 5 c 11 9. xy 3 6 √
z
13
Exercise 26 (Page 48)
10.
1
ef 2 11. a 11/6 b 1/3 c −3/2 or
6√
a
11 3 √
b
√
c
3
1. 1 2. 2 3. 6 4. −4 5. 1 2 3
6. 1 7. 2 8.
1
2
9. 0 10. 3
Exercise 23 (Page 43)
1. 3x + y 2. 3a + 5y 3. 5(x − y)
4. x(3x − 3 + y) 5. −5p + 10q − 6r
6. a 2 + 3ab + 2b 2 7. 3p 2 + pq − 2q 2
8. (i) x 2 − 4xy + 4y 2 (ii) 9a 2 − 6ab + b 2
9. 3ab + 7ac − 4bc 10. 0 11. 4 − a
12. 2 + 5b 2 13. 11q − 2p
14. (i) p(b + 2c) (ii) 2q(q + 4n)
15. (i) 7ab(3ab − 4) (ii) 2xy(y + 3x + 4x 2 )
16. (i) (a + b)(y + 1) (ii) (p + q)(x + y)
17. (i) (x − y)(a + b) (ii) (a − 2b)(2x + 3y)
Exercise 24 (Page 44)
1.
1
2 + 6x 2. 1
5
3. 4a(1 − 2a) 4. a(4a + 1)
5. a(3 − 10a) 6.
7.
9.
11.
2
− 3y + 12
3y
2
3y + 12 1 3 − 5y 8. 2
+ 12 − 13y
3y
5
y + 1
10. pq
( )
1
1
2 (x − 4) 12. y 2 + 3y
Exercise 25 (Page 46)
1. (a) 15 (b) 78
11. 2 12. −10 13. 6 14. −2 15. 2 1 2
16. 2 17. 6 1 4
18. −3
Exercise 27 (Page 50)
1. 5 2. −2 3. −4 1 2
4. 2
5. 12 6. 15 7. −4 8. 5 1 3
9. 2 10. 13 11. −10 12. 2
13. 3 14. −11 15. −6 16. 9
17. 6 1 4
18. 3 19. 4 20. 10
21. ±12 22. −3 1 3
23. ±3 24. ±4
Exercise 28 (Page 51)
1. 10 −7 2. 8 m/s 2 3. 3.472
4. (a) 1.8 (b) 30 5. 12p, 17p 6. 800
Exercise 29 (Page 53)
1. 12 cm, 240 cm 2 2. 0.004 3. 30
4. 45 ◦ C 5. 50 6. £208, £160
7. 30 kg 8. 12 m, 8 m 9. 3.5 kN
Exercise 30 (Page 55)
1. d = c − a − b 2. y = 1 c
(t − x) 3. r =
3 2π
4. x = y − c
m
7. R = S − a
S
5. T = I
PR
or 1 − a S
6. R = E I
8. C = 5 (F − 32)
9
2. (a) 0.0075 (b) 3.15 litres (c) 350 K
3. (a) 0.000 08 (b) 4.16 × 10 −3 A (c) 45V
4. (a) 9.18 (b) 6.12 (c) 0.3375
5. (a) 300 × 10 3 (b) 0.375 m 2 (c) 24 × 10 3
6. 1.5 kW
Exercise 31 (Page 57)
1. x = d λ (y + λ) or d + yd λ
2. f =
3F − AL
3
4. t = R − R 0
R 0 α
or
f = F − AL
3
5. R 2 = RR 1
R 1 − R
3. E = Ml2
8yI