Question 1 [50 marks] a) Simplify the following expression completely: ( 4x ys ) ( 3 xy* )' , x#0, y #0, z#0 (10 marks) 432x 5 (x7 4 ) = 2x+6 x-3 b) Simplify the algebraic fractions completely: x#0 (10 marks) x+1 x c) Solve the following for x given that a = 2 and b = 3: (10 marks) 126 + ba a +ba *#0 a x x 25 d) Solve the given equation: In = In y 25- y (10 marks) 3"+2 . 27"-1 e) Simplify the algebraic fraction completely: 3"-2 . 27 "+1 (10 marks) Question 2 [50 marks] 2x-1 x+3 4x a Solve the equation: 4 3 5 (10 marks) b) The rate (in W) at which heat is developed in a filament of an electric light bulb as a function of electric current (in mA): H = 12 - 14/ + 49 i) Plot H as a function of I showing all turning points and intercepts. (5 marks) ii) Determine the range over which H 2 49. (10 marks) iii) What are the values of current when the heat is 9 Watts. (5 marks) c) The forces acting on a link of an industrial robot in an equilibrium position are shown: 840 O (10 marks) F1 F2 5|Page The equations for finding forces Fi and F2 are given by: F + F, = 840 2F -5F, = 0 Solve the equations to find the values of F1 and F2