Please provide a neat solution. You may use a calculator technique but explain the concepts or formula you will use. Thank you.

Items 45-55:

41. A rubber ball is dropped from a height of 15 meters. On each rebound, it rises 2/3 of the height from which it last fell. Find the distance traversed by the ball before it comes to rest. The distance traversed by the ball before it comes to rest. The geometric progression occurs after the first rebound. A 75 B. 80 C. 80 D. 85 42. A funnel in the form of cone is 10 om across the top and 8 om deep. Water is flowing into the tunnel at the rate of 12 cm/sec and out at the rate of 4 om /sec. How fast is the surface of the water rising when it is 5 om deep? A. 0.26 cm/sec C. 0.14 com/sec B. 0.32 cm/sec D. 0.40 cm/sec 43. Determine the simplified form of [cos 2A - (cos A) W(cos A] A -(sec A) C. Sec A -tan AF D. tan A 44. Using Laplace Transform technique, find the transient response of the system describe by the differential equation d'y/dx' + 3dy/dx + 2y = 1, with the initial condition y(0) = 1, dyldx = 1 whent = 0. A 2e* - (3/2je-a ex - 3e-a B. 2et + (3/2je-# . el+ 3e-a 45. The area of the parallelogram is x" and the height is x*. Find the base of the parallelogram. A x B. x C. 2x D. 2x2 48. The symbol ""used in division is called A. Modulus C. Solidus B. Minus D. Obelus 47. The constant "e" is named in honor of A. Euler C. Euclid B. Eigen D. Einstein 48. The surface area of the spherical segment A. Lune C. Wedge B. Zone D. Sector 40. If n is any positive integer, then (n- 1)(n-2)(n- 3) ... (3)(2X1) = en-1 C. n! B. (n- 1) D. (n- 1) 50. It is the 1/8 of the full circle. A. Octa - quadrant C. Octant B. Octagon D. Octave 51. Simplify is A i B. - C. 1 D. -1 52. A man finds the angle of elevation of the top of a tower to be 30'. He walks 85 m nearer the tower and finds its angle of elevation to be 60*. What is the height of the tower? A. 76.31m C. 73.16 m B. 73.31 m D. 73.61 m 53. A statue 3 m high is standing on a base of 4 m high. If an observer's eye is 1.5 m above the ground, how far should he stand from the base in order that the angle subtended by the statue is a maximum? A 341m C. 3.71m B. 3.51m D. 4.41 m 54. Log(3 + 2]) = Ln(3 + 2)/Ln10 A. 0.514+ j.0235 C. 0.556 + j.0255 B. 0.567 + j.0245 D. 0.578 + j.0285 55. The growth of a country energy consumption is 60%. In how many years the growth will be quadruple? A 2 B. 20 C. 18 D. 16 58. The maximum tidal head available for a proposed tidal-power station is 6 m. What must be the area of the tidal bay to generate an average of 1000 MW of power? The formula is P... = 0.219 AH? 106.8 m C. 126.8 m B. 115.8 m D. 133.8 m 1000 = 0.210 x 36 x area 1000 Area = 0.219 x 36 - = 126.8 m 57. The arithmetic and geometric mean of two numbers are 10 and 8 respectively. Find the harmonic mean. A 24 5. 4.4 C. 6.4 D. 8.4 58. Find the maximum volume of a cylinder inscribed in a core of 4 my volume. 1.78 m' 2.78 m DT 1 7 m' 2 87 m