A plane flying with a constant speed of 9 km/min passes over a ground radar station at an altitude of 12 km and climbs at an angle of 45 degrees. At what rate is the distance from the plane to the radar station increasing 5 minutes later? The distance is increasing at km/min.

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Q: Ivar is eagerly watching a black leaf falling straight down towards a point on the ground whose…

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Q: A ladder 13 ft long leans against a vertical wall. If the top slides down at 3 ft/s, how fast is the…

A: Follow the procedure given below.

Q: A man whose eye level is 6 ft above the ground walks toward a billboard at a rate of 2 ft>s. The…

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Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

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Q: A kite 100 feet above the ground moves horizontally at a speed of 10ft/s. At what rate is the angle…

A: Let the horizontal distance be x. From the given data of question: And the diagram is:

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Q: A certain escalator travels at a rate of 13.4 meters per minute, and its angle of inclination is…

A: So from the triangle we have: Answer(a): Vertical component of the velocity is 6.1667 meters per…

Q: A train 220 m long is running with a speed of 59 kmph . In what time wil it pass a man who is…

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Q: A 10 foot ladder is leaning against a wall, with its base 3 feet from the wall. It begins to slide…

A: Given that A 10 foot ladder is leaning against a wall, with its base 3 feet from the wall. It begins…

Q: An airplane is flying at an altitude of 6 miles and passes directly over a radar antenna. When the…

A: Given that,      An airplane is flying at an altitude of 6 miles and passes directly over a radar…

Q: A plane flies at a speed 540 km/hr at a constant height of 10 km. How rapidly is the angle of…

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Q: 19. A 6 foot ladder is sliding down a vertical wall at a rate of 1 foot per second. What is the rate…

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Q: Two cars are traveling along perpendicular roads, car A at 40 mph and car B at 60 mph. At noon, when…

A: Related rates is the change of quantity with respect to time t. Find the rate of change of a certain…

Q: A weather balloon is rising vertically at the rate of 5 meters per second. An observer is standing…

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Q: A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2 feet per…

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Q: A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude…

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Q: a man 6ft tall walks at rate 5ft/sec away from a lamppost that is 13 ft high. At what rate is the…

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Q: When a rocket is 2 kilometers high, it is moving vertically upward at a speed of 300 kilometers per…

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Q: When a rocket is 8 kilometers high, it is moving vertically upward at a speed of 900 kilometers per…

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Q: kite 100 ft. above the ground moves horizontally at the speed of 8ft/sec. At what rate is the angle…

A:

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second,…

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Q: A balloon was rising vertically in the air from the ground level that was 12 feet away from an…

A: Given,  a balloon was rising vertically in the air from the ground level that was 12 feet away from…

Q: A jet ascends at a 10° angle from the horizontalwith an airspeed of 550 mi>hr (its speed along…

A: Given: A jet ascends at a 10° angle from the horizontal with an airspeed of 550 mi>hr. Let x be…

Q: A bird 150 ft above the ground flies horizontally at a speed of 11 ft/s. At what rate is the angle…

A: Given Data: The height of the bird above the ground is: y=150 ft The speed of the bird is: x'=11…

Q: When a rocket is 6 kilometers high, it is moving vertically upward at a speed of 600 kilometers per…

A: Set the height of the rocket be h and angle of elevation from the observer's eye is x. dhdt=600

Q: A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude…

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Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

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Q: A 13-ft ladder is leaning against a house when itsbase starts to slide away. By the time thebase is…

A: Given: length of ladder, L=13 ft distance from base, x = 12 ft dxdt=5 ft/sec

Q: When a rocket is 10 kilometers high, it is moving vertically upward at a speed of 1000 kilometers…

A: To determine the rate of change of angle of elevation with respect to observer.

Q: A boy is flying a drone at a constant height of 28 m above the ground. If the drone is moving…

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Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: Two airplanes are flying in the air at the same height. Airplane A is flying east at 494 mi/h and…

A: Point A represents position of airplane A. Point B represents position of airplane B.Point C…

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per…

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Q: A kite 100 ft above the ground moves horizontally at a speed of 4 ft/s. At what rate is the angle…

A: Here we use trigonometric formulas along with differentiation formulas.

Q: An airplane is flying on a horizontal path at the height of 3,800 feet. At what rate is the distance…

A: We need to find rate of distance changing.   ddθ(cscθ)=-csc(θ)cot(θ)

Q: You are videotaping a race from a stand 132 ft from the track, following a car that is moving at…

A: Form the situation on a right triangle and use trigonometric ratio than differentiate.

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

A: Let, the angle θ is an acute angle made by telescope and the vertical. The distance between the boat…

Q: A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude…

A:

Q: An observer who is 3km from a launchpad watches a rocket that is rising vertically. At a certain…

A: Rate of change

Q: A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude…

A: given data  constant speed = 24 km/min             altitude = 12 km             angle = 25 degrees…

Q: A kite is flying 25 meters above the flat Earth and being blown by the wind in the horizontal…

A: To calculate rate of change of angle between kite and grounds.  Let theta is the angle between kite…

Q: a television camera is positioned o the ground 4000 feet from the base of a rocket launching pad. If…

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Q: A plane flying with a constant speed of 19 km/min passes over a ground radar station at an altitude…

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Q: A hot air balloon is tethered at an angle of elevation of a/6. The rope holding the balloon is being…

A: Given Data: The angle of elevation is: α=π6 The rate at which the rope is being brought is: dxdt=-4…

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

Q: A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude…

A: