Basic Engineering Mathematics, Fifth Edition

Chapter 10 Further algebra 10.1 Introduction In this chapter, the use of brackets and factorization with algebra is explained, t ...

Further algebra 69 Problem 7. Remove the brackets from the expression and simplify 2[x^2 − 3 x(y+x)+ 4 xy] 2[x^2 − 3 x(y+x)+ 4 x ...

70 Basic Engineering Mathematics (i) What multipliesato makeab?Answer:b (ii) What multipliesato make− 5 ac?Answer:− 5 c Hence,b− ...

Further algebra 71 (x+ 3 )is now a common factor. Thus, x^2 (x+ 3 )− 1 (x− 3 )=(x+ 3 )(x^2 − 1 ) Now try the following Practice ...

72 Basic Engineering Mathematics Problem 22. Simplify 5 a+ 3 a× 2 a+a÷ 2 a− 7 a 5 a+ 3 a× 2 a+a÷ 2 a− 7 a = 5 a+ 3 a× 2 a+ a 2 a ...

Chapter 11 Solving simple equations 11.1 Introduction 3 x−4isanexampleofanalgebraic expression. 3 x− 4 =2isanexampleofanalgebrai ...

74 Basic Engineering Mathematics Note that subtracting 3 from both sides of the above equation results in the +3 moving from the ...

13 Solving simultaneous equations Now try the following Practice Exercise PracticeExercise 42 Solving simple equations (answers ...

76 Basic Engineering Mathematics i.e.^38 y=−^114 Dividing both sides by 38 gives 38 y 38 = − 114 38 Cancelling gives y=− 3 which ...

Solving simple equations 77 8. 2 a = 3 8 9. 1 3 n + 1 4 n = 7 24 10. x+ 3 4 = x− 3 5 + 2 11. 3 t 20 = 6 −t 12 + 2 t 15 − 3 2 12. ...

78 Basic Engineering Mathematics Using a calculator,gas constant,R=4160J/(kg K), correct to 4 significant figures. Problem 20. A ...

Solving simple equations 79 Now try the following Practice Exercise PracticeExercise 44 Practicalproblems involving simple equat ...

80 Basic Engineering Mathematics 8. 40 x= 319. 20 − 226. 80 = 92. 40 x= 92. 40 8. 40 = 11 Thus, 11 hours overtime would have to ...

Solving simple equations 81 An alloy contains 60% by weight of copper, the remainder being zinc. How much copper must be mixed ...

Revision Test 4: Algebra and simple equations This assignment covers the material contained in Chapters 9–11.The marks available ...

Chapter 12 Transposing formulae 12.1 Introduction In the formulaI= V R ,Iis called thesubject of the formula. Similarly, in the ...

84 Basic Engineering Mathematics Rearranging gives^2 gh=v^2 Dividing both sides by 2ggives 2 gh 2 g = v^2 2 g Cancelling gives h ...

Transposing formulae 85 I=PRT (T) XL= 2 πfL (L) I= E R (R) y= x a + 3 (x) F= 9 5 C+ 32 (C) XC= 1 2 πfC (f) 12.3 Further ...

86 Basic Engineering Mathematics Whenever the prospective new subject is a squared term,thattermisisolatedontheLHSandthenthesqua ...

Transposing formulae 87 Taking the cube root of both sides gives √ 3 r^3 =^3 √( 3 V 2 π ) i.e. r=^3 √( 3 V 2 π ) (b) WhenV=32cm^ ...