B6 (a) If (x 1), (x+2) and (x-2) are factors of x3 + ax+ bx +...

 

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B6 (a) If (x 1), (x+2) and (x-2) are factors of x3 + ax+ bx + c, find the values of a, b, and c. (9 marks) 2 (b) Prove the identity tan 20 = and hence, solve cot 0-tane (8 mar' 2 = 1 for 002. 2 cot 0-tane (c) The formula for measuring sound intensity in decibels S is (3 marks) B7 (a) defined as: I S = 10 logo where: I is the intensity of the sound in watts per square meter; and Io 10-12 is the lowest intensity of the sound in watts per square meter that the average person can hear. How many decibels are emitted from a jet plane with a sound intensity (1) of 9 x 10 watts per square meter? The position of a particle moving measured from the x axis (in m) is governed by the equation y = 9t-2.5, where t is the time in seconds. Find: (i) the position of the particle when v = 0m/s; (ii) the instantaneous velocity at t = 2s and t = 3s; (iii) the distance travelled when the particle is between its positions from t = 2s to t = 3s; (iv) the time when its velocity is 3.5m/s. (b) (3 marks) (2 marks) (3 marks) (2 marks) Find the equations of the tangent and normal to the equation: (10 marks) y = (15 3x2)Inx when x = 1. B6 (a) If (x 1), (x+2) and (x-2) are factors of x3 + ax+ bx + c, find the values of a, b, and c. (9 marks) 2 (b) Prove the identity tan 20 = and hence, solve cot 0-tane (8 mar' 2 = 1 for 002. 2 cot 0-tane (c) The formula for measuring sound intensity in decibels S is (3 marks) B7 (a) defined as: I S = 10 logo where: I is the intensity of the sound in watts per square meter; and Io 10-12 is the lowest intensity of the sound in watts per square meter that the average person can hear. How many decibels are emitted from a jet plane with a sound intensity (1) of 9 x 10 watts per square meter? The position of a particle moving measured from the x axis (in m) is governed by the equation y = 9t-2.5, where t is the time in seconds. Find: (i) the position of the particle when v = 0m/s; (ii) the instantaneous velocity at t = 2s and t = 3s; (iii) the distance travelled when the particle is between its positions from t = 2s to t = 3s; (iv) the time when its velocity is 3.5m/s. (b) (3 marks) (2 marks) (3 marks) (2 marks) Find the equations of the tangent and normal to the equation: (10 marks) y = (15 3x2)Inx when x = 1.