ABSTRACT
R = E− e I
− r
21. b= √( y
) 22. L = gt
23. u= √v2 − 2as 24. a = N2y− x
25. L = √ Z2 −R2 2πf
, 0.080
1. apple=8p, banana=35 p 2. apple=28p, orange=17 p 3. car=£15000, van=£12000 4. F1 = 1.5, F2 = −4.5 5. a = 5, b= 2 6. a = 6, b= −1
1. (a) 34.377◦ (b) 45.837◦ (c) 114.592◦ (d) 180◦
2. (a) π
4 rad or 0.7854 rad (b)
π
2 rad or 1.5708 rad
(c) 2π 3 rad or 2.0944 rad (d) π rad or 3.1416 rad
1. (a) 0.5000, 0.8660, 1.7321 (b) 0, 1, ∞ (c) −0.8660, 0.5000, −0.5774 (d) −1, 0, 0 (e) −0.8660, −0.5000, 0.5774 (f) 0, −1, −∞ (g) 0.8660,−0.5000, −0.5774 (h) 0.8660,−0.5000, −0.5774 (i) 0.5000, 0.8660, 1.7321 (j) 0, 1, ∞ (k) −0.8660, 0.5000,−0.5774
1. 35.54◦ 2. 62.61◦ 3. 28.97◦ 4. 7.08cm 5. 4.65m
1. A = 38.96◦, C = 41.04◦, a = 3.83m 2. b= 22.01m, A = 38.86◦, C = 74.14◦ 3. 28.96◦
4. A = 83.33◦, B = 52.62◦, C = 44.05◦ 5. P = 39.73◦, QR = 7.38m
1. log6 2. log15 4. log3 5. log12 7. log100 8. log6 10. log1= 0 11. x = 13. b= 2 14. x = 2
1. 1.690 2. 3.170 3. 4. 2.251 5. 2.542 6. 7. 316.2
1. −0.4904 2. −0.5822 3. 2.197 4. 816.2 5. 0.8274 6. 1.962 7. 3 8. 4 9. 500
10. W = PVln ( U2 U1
)
1. (a) 150◦C (b) 100.5◦C
2. (a) 29.32 volts (b) 71.31× 10−6 s 3. (a) 1.993m (b) 2.293m
4. (a) 3.04A (b) 1.46 s
5. (a) 7.07A (b) 0.966 s
1. (a) −1 (b) −8 (c) −1.5 (d) 4 2. 14.5 3. (a) −1.1 (b) −1.4 4. 1010 rev/min should be 1070 rev/min;
(a) 1000 rev/min (b) 167 V
1. Missing values:−0.75, 0.25, 0.75, 1.75, 2.25, 2.75, Gradient= 12 or 0.5
2. (a) 4, −2 (b) −1, 0 (c) −3, −4 (d) 0, 4 3. (2, 1)
4. (a) 89 cm (b) 11 N (c) 2.4 (d) # = 2.4W+ 48
1. (a) 40◦C (b) 128
2. (a) 0.25 (b) 12 (c) F = 0.25L+ 12 (d) 89.5N (e) 592N (f) 212N
3. (a) 850 rev/min (b) 77.5V
4. (a) 15 or 0.2 (b) 6 (c) E = 0.2L+ 6 (d) 12N (e) 65N
1. (a) 80 m (b) 170 m 2. 27.2 cm2
3. 18 cm 4. 1200 mm 5. (a) 29 cm2 (b) 650 mm2 6. 560 m2
7. 6750 mm2 8. 43.30 cm2
11. (a) 50.27 cm2 (b) 706.9 mm2 (c) 3183 mm2
12. (a) 53.01 cm2 (b) 129.9 mm2
13. 5773 mm2 14. 1.89 m2
15. (a) 0.698 rad (b) 804.2 m2
16. 10.47m2
1. 4.563 square units (using 6 intervals)
2. 54.5 square units (using 8 intervals)
1. 600 N 2. 5.1 kN 3. 8 kg
4. 14.72 N 5. 8 J 6. 12.5 kJ
7. 4.5 W 8. (a) 29.43 kN m (b) 981 W
9. 1000 C 10. 30 s 11. 900 C
12. 5 minutes
13. (a) 1 nF (b) 20 000 pF (c) 5 MHz
(d) 0.047 M (e) 320 μA
1. (a) 0.1 S (b) 0.5 mS (c) 500 S
2. 20 k 3. 1 kW 4. 7.5 W
5. 1 V 6. 7.2 kJ 7. 10 kW, 40 A
1. 5 s 2. 3600 C 3. 13
1. 7 2. (a) 0.25 A (b)
3. 2 m, 5 m 4.
