1. A 15-meter ladder is resting against a vertical wall. If the bottom of the ladder is being pushed horizontally towards the wall at 1.5 m/s, what is the rate of change of the acute angle made by the ladder with the wall when the upper end is 10m above the ground?

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

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Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Given that, the length of the ladder is 10 ft and distance between the wall and ladder in base is 6…

Q: 8.A kite at an altitude of 200 ft. moves horizontally at the rate of 20 ft/sec. At what rate is the…

A: We have to find the rate of change of angle.

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: 11. If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 1. A boy is blowing a spherical balloon at a rate of 50 cm /s. At what rate is the radius of the…

A: This question is based on application of derivative.

Q: 20. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the…

A: Given : A kite is 100 ft above the ground moves horizontally at a speed of  8 ft/s. To find : At…

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A:

Q: A spy uses a telescope to track a rocket launched vertically from a launching pad 6 km away, as in…

A: Given that

Q: A hot-air balloon is 140 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Given the height in which the hot air balloon placed above the ground is 140 ft. Velocity of the…

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

A:

Q: A​ hot-air balloon is 190 ftabove the ground when a motorcycle​ (traveling in a straight line on a…

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the…

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A:

Q: 7. A 6ft tall human is walking away from a 20ft lamppost. Given that the length of the shadow of the…

A: Let the distance of the person from the bottom of the light post be x. Let the length of the shadow…

Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A:

Q: A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the distance of the balloon from point B be denoted as p. The balloon, points A and B form a…

Q: If a ladder of length 20 ft which is leaning against a vertical wall has its upper end sliding down…

A: Given:         Length of ladder =20 ft    dhdt=-2 ft/sec

Q: An inverted conical water tank with a height of 12ft and a radius of 6ft ft is drained through a…

A:

Q: Given a cylinder surmounted on both ends by a hemisphere, find the rate of change of its volume with…

A: Given:     Cylinder is surmounted by hemisphere at both ends.And height of cylinder is 5 meter.

Q: 21. For the camera and rocket shown in Figure 3.4.5, at what rate is the camera-to-rocket distance…

A: Given that the distance between camera and launching pad is 3000 ft., the distance between launching…

Q: A hot air balloon rising vertically is tracked by an observer located 3 miles from the lift-off…

A:

Q: 9. A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: A ball is being launched into the air. 21 feet away from the launch site is a camera. If the ball is…

A: Suppose y represents the height of the ball and θ be the angle of elevation.As the ball is…

Q: A 50-ft ladder is placed against a large building. The base of the ladder is resting on an oil…

A: Given: The length of ladder is 50ft. and rate of change in length of base is 3 ft. per minute i.e.…

Q: 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is…

A:

Q: If a ladder of length 20 ft which is leaning against a vertical wall has its upper end sliding down…

A:

Q: 12. A 7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 f/sec. Assume the…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

A: Given: x=5 km θ=π5 raddθdt=0.3 rad/min The person and the hot air balloon form a right triangle,…

Q: A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Rate of change

Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

A:

Q: 12) A vertical cylinder is leaking wader at a rate I ft3% If the cylinder har a height of 10t Sec.…

A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

Q: 1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3…

A: Authoring guidelines:…

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

A:

Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: Initially, 2 cars are parked side by side on a big field. Then, Car 1 starts to move directly to the…

A: Solution

Q: 5. Assume that an airplane is flying toward you at a constant height of 2 miles and at a speed of…

A: Here we solve this question using differentiation and basic trigonometric formulas.…

Q: A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

A: Given: A 10​-ft ladder is leaning against a house when its base starts to slide away. By the…

Q: A man walks along a straight path at a speed of 4ft/s. A spotlight is located on the ground 20ft…

A:

Q: A man 6 feet tall walks at a rate of 3 feet per second away from a light that is 15 feet above the…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Given that a hot air balloon is rising vertically is tracked by an observer located 7km from the…

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: Suppose the area A of a particular rectangle increases at a rate of 2 cm^2/sec and the width w of…

A:

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: Given,1f=1p+1qwhere f is focal lenrth and an object is placed at a distance p from the lens and its…

Q: A hot air balloon is 120 ft. above the ground when a motorcycle (travleing in a straight line on a…

A: Given that, A hot air balloon is 120 ft. above the ground when a motorcycle (traveling in a straight…

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

A:

Q: 5. A conical tank (with vertex down) is 20 feet across the top and 24 feet deep. If water is flowing…

A: A conical tank is 20 feet across the top and 24 feet deep. If water is flowing into the tank at a…

Q: 1. A 13-ft ladder is leaning against a house when its base is being pushed towards the wall. By the…

A:

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.