A rotating beacon is located 3 miles out in the water. Let A be the point on the shore that is closest to the beacon. As the beacon rotates at 10 rev/min, the beam of light sweeps down the shore once each time it revolves. Assume that the shore is straight.

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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: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

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Q: A 5 foot girl is walking toward a 20-foot lamppost at the rate of 6 feet per second. How fast is the…

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Q: A kite 160 feet above the ground moves in a direction parallel to the ground at the rate of 5 feet…

A: Let, x= the horizontal distance of the kite y=the length of the string Given that dx/dt=5 ft/sec  We…

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 ladder 10 ft long leans against a building. If the bottom of the ladder slides away from the…

A: Given A ladder 10 ft long leans against a building. If the bottom of the ladder slides away from the…

Q: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

A: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

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Q: A 46 ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

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A: It is given that the acceleration of the gravity is 1.6m/sec2.

Q: A street light is mounted at the top of a 15 foot tall pole. A man 6 feet tall walks away from the…

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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:

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: A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground…

A: Given:- A 17 feet ladder is leaning against a wall. if the bottom of the ladder is pulled along the…

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

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Q: An 8 ft ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

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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 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: The top of a 22 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

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Q: A ladder is 20 feet long leaning against the wall of a house, forming a right triangle. The base of…

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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 15-foot ladder is leaning against a mango tree. If the top of the ladder is sliding down the tree…

A: We need to find rate of bottom of ladder moving.

Q: A man 6 ft tall walks along a level sidewalk away from a lamppost. On the post is a street light 18…

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Q: A 12-meter plank is leaning against the wall. If the bottom of the plank is pulled away from the…

A: We need to find how fast the plank will move.

Q: The base of a 13 foot ladder that is leaning against a wall begins to slide away from the wa When…

A: It is given that, length of the ladder x = 13 feet,  The distance between the foot of the ladder and…

Q: How fast is the bottom of the ladder moving along the ground

A: The rate of change is represented by derivative. Therefore the solution would be found by using the…

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

A: A ladder with 10 ft resting on a wall is shown in below figure.

Q: A 10-meter ladder is leaning against the wall of a building. It begins to slide down the wall. When…

A: Let l denote the length of the ladder leaning against the wall of a building Let x denote the…

Q: A ladder 14 ft long rests against a vertical wall. Let 0 be the angle between the top of the ladder…

A: Given:

Q: A 10-ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A: GivenA 10-ft ladder is leaning against wall .{ HereAB is wallAC is ladder }Let the height of the…

Q: An 8 ft. ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall…

A:

Q: A ladder 20 feet long is leaning against an embankment inclined 60 degrees to the horizontal. if the…

A: The ladder is leaning against an embankment inclined 60 degrees to the horizontal has length 20…

Q: A 14 ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A: Definition used -                Related rate -  These are the problems in which we know one of…

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: Let x be the distance between wall and bottom of ladder and y be the distance of top of ladder from…

Q: What constant acceleration is required to increase the speedof a car from 30 mih to 50 mih in 5 s?

A: Given: u=30 mihour, v=50 mihour, t=5 second for finding acceleration, first we convert given…

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

A: To determine the rate of change of angle between the ladder and the ground.

Q: A 6ft tall man is walking away from a 15ft tall street lamp at the rate of 5 ft/sec. How fast is his…

A: topic - triangles and rate

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 man walks along a straight path at a speed of 4ft/s. A searchlight is located on the ground 30…

A: Given data is : dxdt=4 ft/sec To find the Rate of the searchlight is rotating

Q: A man 5 ft tall is walking along a straight line at a rate of 3 ft/sec towards a lamp post that is…

A: According to the given question,

Q: A revolving beacon is situated 3600 feet off a straight shore. If the beacon turns at 2 revolutions…

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Q: A lighthouse is located on a small island 3 km away fromthe nearest point P on a straight shoreline…

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Q: A ladder 20 ft long is leaning against an embankment inclined 60° to the horizontal. If the bottom…

A: Let x= distance of ladder from the embankment, y= vertical height. Given: dxdt=-1 ft/sec To find:…

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 ladder 9 ft long rests agains a vertical wall. If the bottom of the ladder slides away from the…

A: Let the distance between base B of the wall and bottom of the ladder C, BC= x feet  And the angle…

Q: A ladder 25 feet long is leaning against a vertical wall. If the bottom of the ladder is pulled…

A: A ladder 25 feet long is leaning against a vertical wall. The bottom of the ladder is pulled…

Q: A tiger is 45 ft directly south of a herd of elephants. The tiger starts to slink towards the…

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Q: A 22-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the…

A: Leader is leaning against wall at AC=22 ft. Distance of the ladder from the wall is x=15 ft. Let the…