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44. Using Laplace Transfom technique, find the transient response of the system describe by the differential equation Fyldx + 3dyldx +2y = 1, with the initial condition y(0) =1, dyldx = 1 when t=0. A 2e-(3/2)ea B. 2e+ (3/2jea C. e-3e D. e+ 3ea

44. Using Laplace Transfom technique, find the transient response of the system describe by the differential equation Fyldx + 3dyldx +2y = 1, with the initial condition y(0) =1, dyldx = 1 when t=0. A 2e-(3/2)ea B. 2e+ (3/2jea C. e-3e D. e+ 3ea

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 distanoe traversed by the ball before it comes to rest. The geometric progression occurs after the first rebound. A 75 B. 80 C. 00 D. 85 42. A funnel in the form of cone is 10 am across the top and 8 cm deep. Water is flowing into the tunnel at the rate of 12 cm/sec and out at the rate of 4 cmisec. How fast is the surface of the water rising when it is 5 cm deep? A 0.26 cm/sec B. 0.32 cm/sec C. 0.14 am/sec D. 0.40 cm/sec 43. Determine the simplified fom of [cos 2A - (cos A)V(cos A)* A sec A)" B. tan A С. sec A D. tan A 44. Using Laplace Transfom technique. find the transient response of the system describe by the differential equation Fyldx + 3dyldx + 2y = 1, with the initial condition y(0) = 1, dyldx = 1 when t=0. A 2e-(3/2)ea B. 2e+ (3/2jea C. e-3e D. e+ 3ea 45. The area of the parallelogram is x* and the height is x". Find the base of the parallelogram. A x* B. x С. 2х D. 2 46. The symbol 7"used in division is called A Modulus B. Minus C. Solidus D. Obelus 47. The constant "e is named in honor of. A Euler B. Eigen C. Euclid D. Enstein 48. The surface area of the spherical segment A Lune B. Zone Č. Wedge D. Sector 40. Ifn is any positive integer, then (n- 1)(n- 2\n - 3).(3(2X1) = B. (n-1 D. (n-1) 50. It is the 1/8 of the full circle. A Octa - quadrant B. Octagon C. Octant D. Octave 51. Simplify A'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 A 76.31 m B. 73.31 m C. 73.16 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 3.41 m B. 3.51 m C. 3.71 m D. 4.41 m 54. Log(3 + 21) = Ln(3 +2yLn10 A 0.514 +j0235 0.567 +j024 C. 0.556 + j.0255 D. 0.578 +j.0265 55. The growth of a country energy consumption is 8.9%. In how many years the growth will be quadruple? A 2 В. C. 18 D. 16 58. The maximum tidal head available for a proposed tidal-power station is 6m. What must be the area of the tidal bay to generate an average of 1000 MW of power? The fomula is P. = 0.219 AH A 108.8 m B. 115.8 m 1000 = 0.210 x 36 x area C. 126.8 m D. 133.8 m 1000 Area = = 126.8 m 0.219 x 36 57. The arithmetic and geometric mean of two numbers are 10 and 8 respectively. Find the hamonic mean. A 24 5. 4.4 C. 6.4 D. 8.4 58. Find the maximum volume of a cylinder insoribed in a core of 4 m volume. A 1.78 m R 1 87 m C. 2.78 m D 2 87 m
Transcribed Image Text: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 distanoe traversed by the ball before it comes to rest. The geometric progression occurs after the first rebound. A 75 B. 80 C. 00 D. 85 42. A funnel in the form of cone is 10 am across the top and 8 cm deep. Water is flowing into the tunnel at the rate of 12 cm/sec and out at the rate of 4 cmisec. How fast is the surface of the water rising when it is 5 cm deep? A 0.26 cm/sec B. 0.32 cm/sec C. 0.14 am/sec D. 0.40 cm/sec 43. Determine the simplified fom of [cos 2A - (cos A)V(cos A)* A sec A)" B. tan A С. sec A D. tan A 44. Using Laplace Transfom technique. find the transient response of the system describe by the differential equation Fyldx + 3dyldx + 2y = 1, with the initial condition y(0) = 1, dyldx = 1 when t=0. A 2e-(3/2)ea B. 2e+ (3/2jea C. e-3e D. e+ 3ea 45. The area of the parallelogram is x* and the height is x". Find the base of the parallelogram. A x* B. x С. 2х D. 2 46. The symbol 7"used in division is called A Modulus B. Minus C. Solidus D. Obelus 47. The constant "e is named in honor of. A Euler B. Eigen C. Euclid D. Enstein 48. The surface area of the spherical segment A Lune B. Zone Č. Wedge D. Sector 40. Ifn is any positive integer, then (n- 1)(n- 2\n - 3).(3(2X1) = B. (n-1 D. (n-1) 50. It is the 1/8 of the full circle. A Octa - quadrant B. Octagon C. Octant D. Octave 51. Simplify A'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 A 76.31 m B. 73.31 m C. 73.16 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 3.41 m B. 3.51 m C. 3.71 m D. 4.41 m 54. Log(3 + 21) = Ln(3 +2yLn10 A 0.514 +j0235 0.567 +j024 C. 0.556 + j.0255 D. 0.578 +j.0265 55. The growth of a country energy consumption is 8.9%. In how many years the growth will be quadruple? A 2 В. C. 18 D. 16 58. The maximum tidal head available for a proposed tidal-power station is 6m. What must be the area of the tidal bay to generate an average of 1000 MW of power? The fomula is P. = 0.219 AH A 108.8 m B. 115.8 m 1000 = 0.210 x 36 x area C. 126.8 m D. 133.8 m 1000 Area = = 126.8 m 0.219 x 36 57. The arithmetic and geometric mean of two numbers are 10 and 8 respectively. Find the hamonic mean. A 24 5. 4.4 C. 6.4 D. 8.4 58. Find the maximum volume of a cylinder insoribed in a core of 4 m volume. A 1.78 m R 1 87 m C. 2.78 m D 2 87 m
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