A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 16 km and climbs at an angle of 40 degrees. At what rate is the distance from the plane to the radar station increasing 2 minutes later? The distance is increasing at km/min.

Q: A 20-foot-tall tree has fallen against the wall of a garage. The base of the tree starts to slide on…

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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 kite 100 ft above the ground moves horizontally at a speed of 12 ft/s. At what rate is the angle…

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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:

Q: A police cruiser, approaching a right-angled intersection from the north, is chasing a speeding car…

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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 kite 30 m above the ground moves horizontally at a speed of 10 m/min. At what rate is the angle…

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

A:

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

A:

Q: A small rocket is launched straight up in the air at a speed of 4ft/sec. A camera on the ground, 10…

A: Consider the given information. At any time t, rocket is at C tanθ=ACAB=AC10

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

A: The rate of change of a function at a value is equal to the derivative of the function at that…

Q: "A Kite 65 feet above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle…

A: Given a kite 65 feet above the ground moves horizontally at a speed of 6 ft/s.

Q: A ladder 10 ft long leans against a vertical wall. If the bottom of the ladder slides away from the…

A: Given that a ladder 10 ft. long leans against a vertical wall. Bottom of the ladder slides away from…

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

A:

Q: A kite flies at a constant height of 30 meters above the ground in a wind that blows it horizontally…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

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Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: →cosθ = BaseHypotenuse→sinθ = 1-cos2θ→dcosθdθ = -sinθ

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

A:

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: A plane flying with a constant speed of 9 km/min passes over a ground radar station at an altitude…

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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: A flying kite is 100 m above the ground, moving in a horizontal direction at a rate of 10 m/s. How…

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Q: man 6 ft tall walks at a rate of 5 feet per second away from a light that is 15 ft above the ground.…

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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…

A:

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: 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: A woman 5ft tall walks at a rate of 7ft/sec toward a street light that is 12ft above the ground. At…

A: Given A woman 5ft tall walks at a rate of 7ft/sec toward a street light that is 12ft above the…

Q: A kite 100 ft above the ground moves horizontally at a speed of 3 ft/s. At what rate is the angle…

A: The diagrammatic representation of the problem is shown below.

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 ladder 10 ft long leans against a vertical wall. If the bottomof the ladder slides away from the…

A: Given - A ladder 10 ft. long leans against a vertical wall. If the bottom of the ladder slides away…

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

A:

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

A: