Answers to practice exercises 347
Chapter 16
Exercise 62 (page 118)
1. (a)
0.1653 (b) 0.4584
(c) 22030
2. (a)
5.0988 (b) 0.064037 (c) 40.446
3. (a) 4.55848 (b) 2.40444 (c) 8.05124
4. (a) 48.04106 (b) 4.07482 (c) −0.08286
5. 2.739
6. 120.7 m
Exercise 63 (page 120)
1. 2.0601
2. (a) 7.389 (b) 0.7408
3. 1 − 2x 2 −
8
3
x 3 − 2x 4
4. 2x 1/2 + 2x 5/2 + x 9/2 +
1
3
x 13/2
+
1
12
x
17/2
+
1
60
x
21/2
Exercise 64 (page 122)
1. 3.95, 2.05
2. 1.65, −1.30
3. (a) 28 cm 3 (b) 116 min 4. (a) 70 ◦ C (b) 5 minutes
Exercise 65 (page 124)
1. (a) 0.55547 (b) 0.91374 (c) 8.8941
2. (a) 2.2293 (b) −0.33154 (c) 0.13087
3. −0.4904 4. −0.5822 5. 2.197
6. 816.2
7. 0.8274 8. 11.02
9. 1.522 10. 1.485
11. 1.962 12. 3
13. 4
14. 147.9 15. 4.901 16. 3.095
17. t = e
b+a ln D
= e
b e
a ln D
= e
b e
ln D a i.e. t = e
b D
a
18. 500 19. W = PV ln
U 2
U 1
Exercise 66 (page 127)
1. (a) 150 ◦ C (b) 100.5 ◦ C
2. 99.21 kPa
3. (a) 29.32 volts (b) 71.31 × 10 −6 s
4. (a) 1.993 m (b) 2.293 m 5. (a) 50 ◦ C (b) 55.45 s
6. 30.37 N
7. (a) 3.04 A (b) 1.46 s
8. 2.45 mol/cm 3
9. (a) 7.07 A (b) 0.966 s
10. £2424
Chapter 17
Exercise 67 (page 134)
1. (a) Horizontal axis: 1 cm = 4 V (or 1 cm = 5 V),
vertical axis: 1 cm = 10
(b) Horizontal axis: 1 cm = 5 m, vertical axis:
1 cm = 0.1 V
(c) Horizontal axis: 1 cm = 10 N, vertical axis:
1 cm = 0.2 mm
2. (a) −1 (b) −8 (c) −1.5 (d) 5
3. 14.5
4. (a) −1.1 (b) −1.4
5. The 1010 rev/min reading should be 1070 rev/min;
(a) 1000 rev/min (b) 167 V
Exercise 68 (page 140)
1. Missing values: −0.75, 0.25, 0.75, 2.25, 2.75;
Gradient =
1
2
2. (a) 4, −2 (b) −1, 0 (c) −3, −4 (d) 0, 4
3. (a) 2,
1
2
(b) 3, −2
1
2
(c)
1
24
,
1
2
4. (a) 6, −3 (b) −2, 4 (c) 3, 0 (d) 0, 7
5. (a) 2, −
1
2
(b) −
2
3
, −1
2
3
(c)
1
18
, 2 (d) 10, −4
2
3
6. (a)
3
5
(b) −4 (c) −1
5
6
7. (a) and (c), (b) and (e)
8. (2, 1) 9. (1.5, 6) 10. (1, 2)
11. (a) 89 cm (b) 11 N (c) 2.4 (d) l = 2.4 W + 48
12. P = 0.15 W + 3.5 13. a = −20, b = 412
Exercise 69 (page 144)
1. (a) 40 ◦ C (b) 128
2. (a) 850 rev/min (b) 77.5 V
3. (a) 0.25 (b) 12 (c) F = 0.25L + 12
(d) 89.5 N (e) 592 N (f) 212 N
4. −0.003, 8.73
5. (a) 22.5 m/s (b) 6.43 s (c) v = 0.7t + 15.5
6. m = 26.9L − 0.63
7. (a) 1.31 t (b) 22.89% (c) F = −0.09 W + 2.21
8. (a) 96 × 10
9 Pa (b) 0.00022 (c) 28.8 × 10
6 Pa
Chapter 16
Exercise 62 (page 118)
1. (a)
0.1653 (b) 0.4584
(c) 22030
2. (a)
5.0988 (b) 0.064037 (c) 40.446
3. (a) 4.55848 (b) 2.40444 (c) 8.05124
4. (a) 48.04106 (b) 4.07482 (c) −0.08286
5. 2.739
6. 120.7 m
Exercise 63 (page 120)
1. 2.0601
2. (a) 7.389 (b) 0.7408
3. 1 − 2x 2 −
8
3
x 3 − 2x 4
4. 2x 1/2 + 2x 5/2 + x 9/2 +
1
3
x 13/2
+
1
12
x
17/2
+
1
60
x
21/2
Exercise 64 (page 122)
1. 3.95, 2.05
2. 1.65, −1.30
3. (a) 28 cm 3 (b) 116 min 4. (a) 70 ◦ C (b) 5 minutes
Exercise 65 (page 124)
1. (a) 0.55547 (b) 0.91374 (c) 8.8941
2. (a) 2.2293 (b) −0.33154 (c) 0.13087
3. −0.4904 4. −0.5822 5. 2.197
6. 816.2
7. 0.8274 8. 11.02
9. 1.522 10. 1.485
11. 1.962 12. 3
13. 4
14. 147.9 15. 4.901 16. 3.095
17. t = e
b+a ln D
= e
b e
a ln D
= e
b e
ln D a i.e. t = e
b D
a
18. 500 19. W = PV ln
U 2
U 1
Exercise 66 (page 127)
1. (a) 150 ◦ C (b) 100.5 ◦ C
2. 99.21 kPa
3. (a) 29.32 volts (b) 71.31 × 10 −6 s
4. (a) 1.993 m (b) 2.293 m 5. (a) 50 ◦ C (b) 55.45 s
6. 30.37 N
7. (a) 3.04 A (b) 1.46 s
8. 2.45 mol/cm 3
9. (a) 7.07 A (b) 0.966 s
10. £2424
Chapter 17
Exercise 67 (page 134)
1. (a) Horizontal axis: 1 cm = 4 V (or 1 cm = 5 V),
vertical axis: 1 cm = 10
(b) Horizontal axis: 1 cm = 5 m, vertical axis:
1 cm = 0.1 V
(c) Horizontal axis: 1 cm = 10 N, vertical axis:
1 cm = 0.2 mm
2. (a) −1 (b) −8 (c) −1.5 (d) 5
3. 14.5
4. (a) −1.1 (b) −1.4
5. The 1010 rev/min reading should be 1070 rev/min;
(a) 1000 rev/min (b) 167 V
Exercise 68 (page 140)
1. Missing values: −0.75, 0.25, 0.75, 2.25, 2.75;
Gradient =
1
2
2. (a) 4, −2 (b) −1, 0 (c) −3, −4 (d) 0, 4
3. (a) 2,
1
2
(b) 3, −2
1
2
(c)
1
24
,
1
2
4. (a) 6, −3 (b) −2, 4 (c) 3, 0 (d) 0, 7
5. (a) 2, −
1
2
(b) −
2
3
, −1
2
3
(c)
1
18
, 2 (d) 10, −4
2
3
6. (a)
3
5
(b) −4 (c) −1
5
6
7. (a) and (c), (b) and (e)
8. (2, 1) 9. (1.5, 6) 10. (1, 2)
11. (a) 89 cm (b) 11 N (c) 2.4 (d) l = 2.4 W + 48
12. P = 0.15 W + 3.5 13. a = −20, b = 412
Exercise 69 (page 144)
1. (a) 40 ◦ C (b) 128
2. (a) 850 rev/min (b) 77.5 V
3. (a) 0.25 (b) 12 (c) F = 0.25L + 12
(d) 89.5 N (e) 592 N (f) 212 N
4. −0.003, 8.73
5. (a) 22.5 m/s (b) 6.43 s (c) v = 0.7t + 15.5
6. m = 26.9L − 0.63
7. (a) 1.31 t (b) 22.89% (c) F = −0.09 W + 2.21
8. (a) 96 × 10
9 Pa (b) 0.00022 (c) 28.8 × 10
6 Pa