Basic Engineering Mathematics, Fifth Edition

88 Basic Engineering Mathematics Cancelling gives a^2 = rp (x+y) Taking the square root of both sides gives a= √( rp x+y ) Whene ...

Transposing formulae 89 Rearranging gives √( f+p f−p ) = D d Squaring both sides gives ( f+p f−p ) = D^2 d^2 Cross-multiplying,i ...

Chapter 13 Solving simultaneous equations 13.1 Introduction Onlyoneequationisnecessarywhenfindingthevalueof asingle unknown quan ...

Solving simultaneous equations 91 (b) By elimination x+ 2 y=−1(1) 4 x− 3 y= 18 (2) If equation (1) is multiplied throughout by 4 ...

92 Basic Engineering Mathematics 5 ×equation (1) gives 35 x− 10 y= 130 (3) 2 ×equation (2) gives 12 x+ 10 y= 58 (4) Adding equat ...

Solving simultaneous equations 93 Problem 6. Solve x 8 + 5 2 =y (1) 13 − y 3 = 3 x (2) Whenever fractions are involved in simult ...

94 Basic Engineering Mathematics Now try the following Practice Exercise PracticeExercise 50 Solving simultaneous equations (ans ...

Solving simultaneous equations 95 Subtracting equation (5) from equation (7) gives 43 x+ 0 = 86 x= 86 43 = 2 Substitutingx=2 int ...

96 Basic Engineering Mathematics Substitutingx=2 into equation (3) gives 5 ( 2 )+ 3 y= 1 10 + 3 y= 1 3 y= 1 − 10 =− 9 y= − 9 3 = ...

Solving simultaneous equations 97 Problem 13. The equation of a straight line, of gradientmand intercept on they-axisc,is y=mx+c ...

98 Basic Engineering Mathematics Substitutings=42 andt=2intos=ut+ 1 2 at^2 gives 42 = 2 u+ 1 2 a( 2 )^2 i.e. 42 = 2 u+ 2 a (1) S ...

Solving simultaneous equations 99 Whenc= 52 , T=100, hence 52 =a+ 100 b (1) Whenc= 172 , T=400, hence 172 =a+ 400 b (2) Equation ...

100 Basic Engineering Mathematics Multiplying equation (1) by 4 gives 4 x+ 4 y+ 4 z= 16 (4) Equation (2) – equation (4) gives − ...

Revision Test 5 : Transposition and simultaneous equations This assignment covers the material contained in Chapters 12 and 13.T ...

Chapter 14 Solving quadratic equations 14.1 Introduction As stated in Chapter 11, anequationis a statement that two quantities a ...

Solving quadratic equations 103 The quadratic equationx^2 + 2 x− 8 =0 thus becomes (x+ 4 )(x− 2 )= 0 Since the only way that thi ...

104 Basic Engineering Mathematics Hence, ( 2 x+ 3 )( 2 x+ 1 )=0, from which either ( 2 x+ 3 )=0or( 2 x+ 1 )=0. Thus, 2x=− 3 ,fro ...

Solving quadratic equations 105 14.3 Solution of quadratic equations by ‘completing the square’ An expression such asx^2 or(x+ 2 ...

106 Basic Engineering Mathematics Adding to both sides (half the coefficient ofx)^2 gives x^2 + 9 2 x+ ( 9 4 ) 2 = ( 9 4 ) 2 − 4 ...

Solving quadratic equations 107 Problem 18. Solvex^2 + 2 x− 8 =0byusingthe quadratic formula Comparing x^2 + 2 x− 8 =0 with ax^2 ...