John Bird - Birds Comprehensive Engineering Mathematics

19kg 16m 479mm

-66 -225

-2136 -36121 107701

-4 1487 5914

189g -70872 $15333

d=64mm,A=136mm,B=10mm

(a)468 (b)868 (a)1827 (b)4158

(a)8613 kg (b)584 kg

(a)351mm (b)924mm

(a)10 304 (b) -4433 (a)48 m (b)89 m

(a)259 (b)56 (a)1648 (b) -1060

(a)8067 (b)3347 18 kg

89.25 cm 29

(a)4 (b)24 (a)12 (b)360

(a)10 (b)350 (a)90 (b)2700

(a)2 (b)210 (a)3 (b)180

(a)5 (b)210 (a)15 (b)6300

(a)14 (b)420 420 (a)14 (b)53 900

59 14 88 5 33

22 68 5 2 5

-1

37,49,12,35,58 1115

1730 4377

4763 1115 85152

1940 11621 1760 1720

11

1223 4

13 15 400litres

(a) 60,(b)P36,Q16 2880litres

2118 -19 1320

41920 2

4 21720

1320 9250 6125

(a) 3350 (b) 2125 (c) (d) 141500 (e) 3125

42140 231125 103200 6716

(a) 14150 (b) 41140 (c) 1418 (d) 15720 (e) 161780

0.625 6.6875 0.21875 11.1875

0.28125

1. 14.18
2. 2.785
3. 65.38
4. 43.27
5. 1.297
6. 0.000528

80.3 329.3 72.54 -124.83

295.3 18.3 12.52mm

4.998 47.544 385.02 582.42

456.9 434.82 626.1 1591.6

0.444 0.62963 1.563 53.455

13.84 8.69 (a)24.81 (b)24.812

(a)0.00639 (b)0.0064 (a) 8.4 (b) 62.6

2400

30.797 11927 13.62 53.832

84.42 1.0944 50.330 36.45

10.59 12.325

12.25 0.0361 46.923 1.29610-3

2.4430 2.197 30.96 0.0549

219.26 5.83210-6

0.571 40 0.13459 137.9

14.96 19.4481 515.3610-6

1.0871 15.62510-9 52.70

2.182 11.122 185.82

0.8307 0.1581 2.571

5.273 1.2555 0.30366

1.068 3.5106 37.5103

4.210-6 202.76710-3 18.32106

0.4667 1314 4.458 2.732

0.7083 -910

2.567 0.0776

0.9205 0.7314 2.9042 0.2719

0.4424 0.0321 0.4232 0.1502

-0.6992 5.8452

1. 4.995
2. 5.782
3. 25.72
4. 69.42
5. 0.6977
6. 52.92
7. 591.0
8. 17.90
9. 3.520
10. 0.3770

Order of magnitude error should be 2.1

Rounding-off error should add correct to 4

significant figures or correct to 1 decimal place

Blunder

Measured values, hence c= 55800 Pa m

Order of magnitude error and rounding-off error

should be 0.0225, correct to 3 significant figures or

0.0225, correct to 4 decimal places

30 (29.61 by calculator)

2 (1.988, correct to 4 s.f., by calculator)

10 (9.481, correct to 4 s.f., by calculator)

R I R R I

R I R R R

A=66.59cm2 C=52.78mm R=37.5

159m/s 0.407A 5.02mm

0.144J 628.8m2 224.5

14230kg/m3 281.1m/s 2.526

589.27 508.1W V=2.61V

F=854.5 I=3.81A t=14.79s

E=3.96J I=12.77A s=17.25m

A=7.184cm2 v=7.327

(a)12.53 h (b)1 h 40 min , 33 m.p.h.

(c)13.02 h (d)13.15 h

0.32% 173.4% 5.7% 37.4%

128.5% 0.20 0.0125 68.75%

38.462% (a) 21.2% (b) 79.2% (c) 169%

(b), (d), (c), (a) 1320

A=12 , B=50% , C=0.25 , D=25% , E=0.30 ,

F=310 , G=0.60 , H=60% , I=0.85 , J=1720

779 to 861

21.8kg 9.72m

(a) 496.4,t (b) 8.657g (c) 20.73s 2.25%

(a) 14% (b) 15.67% (c) 5.36% 37.8g

14 minutes 57 seconds 76g

37.49% 39.2% 17% 38.7%

2.7% 5.60m 3.5%

(a) (i) 656 (ii) 984

quad (b) (i) 44.65 k (ii) 49.35 k

2592 rev/min

2.5% 18% 175000

20000 8446.05 50.25

39.60 917.70 185000 7.2%

A0.6kg,B0.9kg,C0.5kg

54%,31%,15%,0.3,t

20000kg (or 20 tonnes)

13.5mm,11.5mm 600kW

36 : 1 3.5 : 1 or 7 : 2 47 : 3

96cm,240cm hours or 5 hours 15 minutes

3680, 1840, 920 12cm 2172

1 : 15 76ml 25% 12.6kg

14.3kg 25000kg

264kg 450N 14.56kg

(a)0.00025 (b) 48MPa (a) 440K (b) 5.76litre

8960

(a) 2mA (b) 25V 434fr 685.8mm

83lb10oz (a) 159.1litres (b) 16.5gallons

29.4MPa 584.2mm $891

3.5 weeks 20 days

(a)9.18 (b)6.12 (c)0.3375 50 minutes

(a) 300103 (b) 0.375m2 (c) 24103Pa

(a) 32 J (b) 0.5 m

27 128 100 000 96

100 1 64

128 16 1 8

100 1000 1100 or 0.01 5

1 25

or 1243 49 or 0.5 1

1352 17337 3225 121052

9 3

147148 -11956 -31345

-1718 64

cubic metre, m3 farad

square metre, m2 metre per second, m/s

kilogram per cubic metre, kg/m3

joule coulomb watt

radian or degree volt mass

electrical resistance frequency

acceleration electric current

inductance length

temperature pressure

angular velocity m,10-3

10-12 M,106

(a) 7.3910 (b) 2.8410 (c) 1.9762102

(a) 2.748103 (b) 3.317104 (c) 2.74218105

(a) 2.40110-1 (b) 1.7410-2 (c) 9.2310-3

(a) 1.7023103 (b) 1.00410 (c) 1.0910-2

(a) 510-1 (b) 1.187510

(c) 1.306102 (d) 3.12510-2

(a)1010 (b)932.7 (c)54100 (d)7

(a)0.0389 (b)0.6741 (c)0.008

(a) 1.35102 (b) 1.1105

(a) 2102 (b) 1.510-3

(a) 2.71103kgm-3 (b) 4.410-1

(c) 3.7673102 (d) 5.1110-1MeV

(e) 9.57897107Ckg-1

(f ) 2.24110-2m3mol-1

60kPa 150W or 0.15mW

50MV 55nF

100kW 0.54mA or 540A

1.5M 22.5mV

35GHz 15pF

17A 46.2k

3A 2.025MHz

50kN 0.3nF

62.50m 0.0346kg

13.510-3 4103

3.8105km 0.053 nm

5.6106 Pa = 5.6 MPa

4.310-3 m = 4.3 mm

2450 mm 167.5 cm 658 mm

25.4 m 56.32 m 4356 mm

87.5 cm (a) 4650 mm (b) 4.65 m

(a) 504 cm (b) 5.04 m

148.5 mm to 151.5 mm

8104 cm 24010-4 m or 0.024 m

3.6 mm 350 10-6 m or 0.35 10-3 m

50000 mm 2.5 cm

(a) 288000 mm (b) 2880 cm (c) 0.288 m

2.5 cm 400 10-6 m

0.87 mm or 870 mm 2.4 m

1500 10-9 m or 1.5 10-6 m

400 10-3 cm or 0.4 cm 6.4 mm

7500 10-3 cm or 7.5 cm