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Calculations and evaluation of formulae 25 4.3 Conversion tables and charts It is often necessary to make calculations from various conversion tables and charts. Examples include currency exchange rates, imperial to metric unit conversions, train or bus timetables, production schedules and so on. Problem 14. Currency exchange rates for five countries are shown in Table 4.1 Table 4.1 France £1 = 1.50 euros Japan £1 = 175 yen Norway £1 = 11.25 kronor Switzerland £1 = 2.20 francs U.S.A. £1 = 1.82 dollars ($) Calculate: (a) how many French euros £27.80 will buy, (b) the number of Japanese yen which can be bought for £23, (c) the pounds sterling which can be exchanged for 6412.5 Norwegian kronor, (d) the number ofAmerican dollars which can be purchased for £90, and (e) the pounds sterling which can be exchanged for 2794 Swiss francs. (a) £1 = 1.50 euros, hence £27.80 = 27.80 × 1.50 euros = 41.70 euros (b) £1 = 175 yen, hence £23 = 23 × 175 yen = 4025 yen (c) £1 = 11.25 kronor, hence 6412.5 kronor = £ 6412.5 11.25 = £570 (d) £1 = 1.82 dollars, hence £90 = 90 × 1.82 dollars = $163.80 (e) £1 = 2.20 Swiss francs, hence 2794 franc = £ 2794 2.20 = £1270 Problem 15. Some approximate imperial to metric conversions are shown in Table 4.2 Table 4.2 length weight capacity 1 inch = 2.54 cm 1 mile = 1.61 km 2.2 lb = 1kg (1 lb = 16 oz) 1.76 pints = 1 litre (8 pints = 1 gallon) Use the table to determine: (a) the number of millimetres in 9.5 inches, (b) a speed of 50 miles per hour in kilometres per hour, (c) the number of miles in 300 km, (d) the number of kilograms in 30 pounds weight, (e) the number of pounds and ounces in 42 kilograms (correct to the nearest ounce), (f ) the number of litres in 15 gallons, and (g) the number of gallons in 40 litres. (a) 9.5 inches = 9.5 × 2.54 cm = 24.13 cm 24.13 cm = 24.13 × 10 mm = 241.3 mm (b) 50 m.p.h. = 50 × 1.61 km/h = 80.5 km/h (c) 300 km = 300 miles = 186.3 miles 1.61 (d) 30 lb = 30 kg = 13.64 kg 2.2 (e) 42 kg = 42 × 2.2lb= 92.4lb 0.4 lb = 0.4 × 16 oz = 6.4 oz = 6 oz, correct to the nearest ounce. Thus 42 kg = 92 lb 6 oz, correct to the nearest ounce. (f ) 15 gallons = 15 × 8 pints = 120 pints 120 pints = 120 litres = 68.18 litres 1.76 (g) 40 litres = 40 × 1.76 pints = 70.4 pints 70.4 pints = 70.4 8 Now try the following exercise Exercise 15 gallons = 8.8 gallons Further problems conversion tables and charts (Answers on page 272) 1. Currency exchange rates listed in a newspaper included the following: Italy £1 = 1.52 euro Japan £1 = 180 yen Australia £1 = 2.40 dollars Canada £1 = $2.35 Sweden £1 = 13.90 kronor Calculate (a) how many Italian euros £32.50 will buy, (b) the number of Canadian dollars that can be purchased for £74.80, (c) the pounds sterling which can be exchanged for 14 040 yen, (d) the pounds sterling which can be exchanged for 1751.4 Swedish kronor, and (e) the Australian dollars which can be bought for £55
26 Basic Engineering Mathematics Table 4.3 Liverpool, Hunt’s Cross and Warrington → Manchester Reproduced with permission of British Rail 2. Below is a list of some metric to imperial conversions. Length Weight Capacity 2.54 cm = 1 inch 1.61 km = 1 mile 1 kg = 2.2 lb (1 lb = 16 ounces) 1 litre = 1.76 pints (8 pints = 1 gallon) Use the list to determine (a) the number of millimetres in 15 inches, (b) a speed of 35 mph in km/h, (c) the number of kilometres in 235 miles, (d) the number of pounds and ounces in 24 kg (correct to the nearest ounce), (e) the number of kilograms in 15 lb, (f) the number of litres in 12 gallons and (g) the number of gallons in 25 litres. 3. Deduce the following information from the BR train timetable shown in Table 4.3: (a) At what time should a man catch a train at Mossley Hill to enable him to be in Manchester Piccadilly by 8.15 a.m.?
Page 2 and 3: Basic Engineering Mathematics
Page 4 and 5: Basic Engineering Mathematics Fourt
Page 6 and 7: Contents Preface xi 1. Basic arithm
Page 8 and 9: Contents vii 13.3 Graphical solutio
Page 10 and 11: Contents ix 27.4 Vector subtraction
Page 12 and 13: Preface Basic Engineering Mathemati
Page 14 and 15: 1 Basic arithmetic 1.1 Arithmetic o
Page 16 and 17: Basic arithmetic 3 12. −23148 −
Page 18 and 19: Basic arithmetic 5 Problem 18. 23
Page 20 and 21: Fractions, decimals and percentages
Page 28 and 29: Indices and standard form 15 From l
Page 30 and 31: Indices and standard form 17 16 2
Page 32 and 33: Indices and standard form 19 3.6 Fu
Page 34 and 35: 4 Calculations and evaluation of fo
Page 36 and 37: Calculations and evaluation of form
Page 44 and 45: Computer numbering systems 31 3. (a
Page 46 and 47: Computer numbering systems 33 11 11
Page 48 and 49: Computer numbering systems 35 Probl
Page 50 and 51: 6 Algebra 6.1 Basic operations Alge
Page 52 and 53: Algebra 39 ) 2a 2 − 2ab − b 2 2
Page 54 and 55: Algebra 41 Using the third and four
Page 56 and 57: Algebra 43 x 2 is a common factor o
Page 58 and 59: Algebra 45 10. p 2 − 3pq × 2p ÷
Page 60 and 61: 7 Simple equations 7.1 Expressions,
Page 62 and 63: Simple equations 49 7.3 Further wor
Page 64 and 65: Simple equations 51 Problem 18. A r
Page 66 and 67: Simple equations 53 Squaring both s
Page 68 and 69: Transposition of formulae 55 Rearra
Page 70 and 71: Transposition of formulae 57 Now tr
Page 72 and 73: Transposition of formulae 59 6. 7.
Page 74 and 75: Simultaneous equations 61 Hence y =
Page 76 and 77: Simultaneous equations 63 It is oft
Page 78 and 79: Simultaneous equations 65 Thus the
Page 80 and 81: Simultaneous equations 67 Substitut
Page 82 and 83: 10 Quadratic equations 10.1 Introdu
Page 84 and 85: Quadratic equations 71 In Problems
Page 86 and 87: Quadratic equations 73 Summarizing:
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Quadratic equations 75 Neglecting t
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11 Inequalities 11.1 Introduction t
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Inequalities 79 i.e. 11.4 Inequalit
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Inequalities 81 Solving quadratic i
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12 Straight line graphs 12.1 Introd
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Straight line graphs 85 Problem 2.
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Straight line graphs 87 (b) Rearran
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Straight line graphs 89 Degrees Fah
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Straight line graphs 91 y 147 140 A
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Straight line graphs 93 Stress (pas
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Graphical solution of equations 95
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14 Logarithms 14.1 Introduction to
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Logarithms 105 i.e. −5 = 4x i.e.
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15 Exponential functions 15.1 The e
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Exponential functions 109 If in the
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Exponential functions 111 Problem 1
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Exponential functions 113 ( ) 5.14
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Exponential functions 115 (b) Trans
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16 Reduction of non-linear laws to
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Reduction of non-linear laws to lin
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Graphs with logarithmic scales 125
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18 Geometry and triangles 18.1 Angu
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Geometry and triangles 133 (d) 227
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Geometry and triangles 135 (a) Equi
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Geometry and triangles 137 Hence XZ
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Geometry and triangles 139 Now try
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Geometry and triangles 141 Assignme
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Introduction to trigonometry 143 Fr
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Introduction to trigonometry 145 Si
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Introduction to trigonometry 147 If
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Introduction to trigonometry 149 To
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20 Trigonometric waveforms 20.1 Gra
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Trigonometric waveforms 153 between
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Trigonometric waveforms 155 45° 60
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Trigonometric waveforms 157 y 4 0 y
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Trigonometric waveforms 159 v rads/
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Trigonometric waveforms 161 Assignm
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Cartesian and polar co-ordinates 16
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Cartesian and polar co-ordinates 16
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Areas of plane figures 167 W X Tabl
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Areas of plane figures 169 (b) Area
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Areas of plane figures 171 14. Calc
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Areas of plane figures 173 is 12 50
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The circle 175 Q B Now try the foll
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The circle 177 From equation (2), a
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The circle 179 Thus, for example, t
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Volumes of common solids 181 Proble
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Volumes of common solids 183 Proble
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Volumes of common solids 185 Fig. 2
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Volumes of common solids 187 From F
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Volumes of common solids 189 Volume
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25 Irregular areas and volumes and
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Irregular areas and volumes and mea
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Triangles and some practical applic
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27 Vectors 27.1 Introduction Some p
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Vectors 209 r 10° b Having obtaine
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Vectors 211 b Fig. 27.11 o Fig. 27.
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Vectors 213 N Thus the velocity of
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Adding of waveforms 215 y 6.1 6 4 2
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Adding of waveforms 217 The horizon
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Number sequences 219 The first four
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Number sequences 221 5. Determine t
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Number sequences 223 Hence 1 ( 1 9
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Number sequences 225 Now try the fo
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Presentation of statistical data 22
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31 Measures of central tendency and
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Measures of central tendency and di
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Measures of central tendency and di
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32 Probability 32.1 Introduction to
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Probability 243 (a) The probability
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Probability 245 Two brass washers a
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33 Introduction to differentiation
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Introduction to differentiation 249
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34 Introduction to integration 34.1
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Introduction to integration 259 ∫
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Introduction to integration 261 Pro
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Introduction to integration 263 A t
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Introduction to integration 265 Ass
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List of formulae 267 (ii) Parallelo
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List of formulae 269 Cartesian and
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Answers to exercises 271 Exercise 7
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Answers to exercises 273 7. ab 6 c
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Answers to exercises 275 5. 0.013 3
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Index Abscissa, 83 Acute angle, 132
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Index 287 Interior angles, 132, 134
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