A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

Q: An airplane is flying west at 500 ft/sec at a constant altitude of 4000 ft and a searchlight on the…

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Q: A rocket, rising vertically, is tracked by a radar station that is on the ground 5 mi from the…

A: Given that: Rate of increase of distance from radar station = 2000 mi/hDistance between radar…

Q: A man 6 ft tall is walking toward a building at the rate of 5 ft/s. There is a light on the ground…

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Q: A lighthouse sits 1 km offshore, and its beam of light rotates counterclockwise at the constant rate…

A: Let x be the image of the beam on the coastline and let theta be the angle as on the given figure.…

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

A: Here we find rate of shadow lengthening.

Q: A street light is fastened to the top of a 15-ft-high pole. If a 5-ft-tall women walks away from the…

A: In the figure,  AB=15 ft DE=5 ft BD=yDC=xdydt=3 ft/sec

Q: A picture 40cm high is placed on a wall with its base 30cm above the level of the eye of an…

A: Shown below

Q: The top of a ladder 30 meters long leans against a vertical wall, and the lower end rests on a level…

A: Let the height of wall corresponding to the ladder lean at any instant be denoted as h. Let 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…

Q: A light is hung 15 ft above a straight horizontal path. if a man 6 ft tall is walking away from the…

A: Solution :x=distance from lights=length of shadowlet,height of light,D=15 ftheight of…

Q: A 10-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

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

A: In the figure, x is the distance of pole from the man at the ground level. s is the length of the…

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

A: To find: The rate of the man shadow moving when he is 30 feet from the post. Given: The height of…

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 man 1.69m m tall i s walking on a horizontal street at 3.2 kph away from a vertical street light,…

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Q: Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If he…

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Q: A man 5ft tall is walking along a straight line at a rate of 3ft/s towards a lamp post that is 15ft…

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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 lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline…

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Q: A man, 1.65 m tall is walking on a horizontal street at 2.3 kph away from a vertical street light,…

A:

Q: A 3-m long steel pipe has its upper end leaning against a vertical wall and the  lower end on a…

A: Given that: Length of steel pipe=3mLower end moves away from the wall at a speed = 2cm/s

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

A:

Q: A ladder 10 feet long is leaning against a wall, with the foot of the ladder 8 feet away from the…

A: To determine the rate at which the ladder is sliding.

Q: A balloon is 30 meters above the ground when a car, running at 40 kph, passes directly below it. It…

A: Given,         A balloon is 30m above the ground when a car, running at 40kph passes directly below…

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: 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: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

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

A: Please refer the attached image for complete solution. THANK YOU !

Q: A lighthouse, L, is on an island 4 mi away from the closest point, P, on the beach. If the…

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Q: pushed

A: Given: A ladder 10 meters long is leaning against a wall. If the bottom of the ladder is being…

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 man that is 5 feet tall is walking in a straight line at a rate of 3 ft / s towards a lamp post…

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Q: A 6-ft tall man is walking towards a 15-ft tall street lamp at the rate of 9 ft/sec. How fast is his…

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Q: A searchlight, 1/2 mi from a straight shore, rotates at the rate of 2 rev/min. How fast is the spot…

A: Let the angle formed by line AB with the line AC is x  in the triangle ABC,   So, from the tangent…

Q: a 5-ft tall person walks away from a 20-ft tall streetlamp at a constant rate of 3 ft/s . at which…

A: Let us denote: x= distance of the person from the post y=length of the shadow Given that, dx/dt=3 ,…

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

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Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

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

A:

Q: A street light is at the top of a 15.0 ft. tall pole. A man 5.8 ft tall walks away from the pole…

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Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A:

Q: How fast is the tip of her shadow moving?

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: A lighthouse is on a small island 4 km from the nearest point P on a straight shoreline. Its beacon…

A: Given: lighthouse is situated on a small island 4 km from point P   number of revolutions= 1…

Q: A man 6 ft. tall is walking towards a building at the rate of 4 ft./sec. If there is a light on the…

A:

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…

A:

Q: A street light is at the top of a 11.0 ft. tall pole. A man 5.8 ft tall walks away from the pole…

A: Given : Height of pole h = 11.0 ft Height of man = 5.8 ft  Man walks away from pole with the speed…

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 man 7.00 ft tall approaches a street light 16.0 ft above the ground at the rate of 6.00 ​ft/s. How…

A: Given data: The height of the man is CD=7 ft. The height of the street light is AB=16 ft. The rate…

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…