A fish is reeled in at a rate of 4.4 feet per second from a point 10 feet above the water. At what rate is the angle between the line and the water changing when there is a total of 25 feet of line out in rad/sec?( round to 3 decimal places)

Q: An airplane is moving horizontally at 150 mph over an observer at a height of 4,000 ft. How fast is…

A:

Q: A beacon that makes one revolution every 13 seconds is located on a ship anchored 4 kilometers from…

A: Given that a beacon that makes one revolution every 13 seconds is located on a ship anchored 4…

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

A:

Q: A tire is rotating 600 times per min. Through how many degrees does a point on the edge of the tire…

A: The circular motion performed by a wheel has an angular speed ω. Angular speed is defined as the…

Q: A plane flying with a constant speed of 300 km/h passesover a ground radar station at an altitude of…

A:

Q: A 18-ft ladder leaning against a wall begins to slide. How fast is the angle between the ladder and…

A: A 18-ft ladder is leaning against the wall. To find how fast the angle between the ladder and the…

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

A: Let the angle be θ between the ladder and the ground.

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

A: Given that, the ladder is 10 ft long ,the rate of change when  ladder slides is 0.7 feet per second.…

Q: When a rocket is 8 kilometers high, it is moving vertically upward at a speed of 600 kilometers per…

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Q: A ladder that is 3 meters long is leaning against a wall. The base of the ladder slides away from…

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

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

A:

Q: A ladder 25 ft long is leaning against a wall. If the bottom of the ladder is pulled 10.…

A: We need to find change in angle.

Q: Find the length of the arc on a circle of radius 10 feet intercepted by a 135° central angle.…

A:

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

A: Given thatLadder length = 10 ftDistance of ladder from the bottom of wall = 6 ftRate of change of…

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

A:

Q: When a rocket is 6 kilometers high, it is moving vertically upward at a speed of 100 kilometers per…

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

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

A:

Q: When a rocket is 7 kilometers high, it is moving vertically upward at a speed of 100 kilometers per…

A: Given:When a rocket is 7 kilometers high, it is moving vertically upward at a speed of 100…

Q: The blades of a fan have a radius of 16.5 in. and they turn one revolution every 0.125 sec.…

A:

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

A:

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

A: Given that:                   Length of ladder = 10ftBottom of the slider slides away from the wall…

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: Find the length of the arc on a circle of radius 20 feet intercepted by a 75° central angle. Express…

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

A: A ladder is given that slides away from the wall we find angle between ladder and the ground…

Q: A fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water. At what…

A: Given: A fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water and…

Q: A straight hiking trail is 2500 ft long with a gain in altitude of 310 ft to the nearest degree what…

A:

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 rests against a vertical wall. If the bottom of the ladder slides away from the…

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

Q: You stand 15 feet from the base of a water tower and look un at an angle of 78° at the top of the…

A: Draw the whole situation and mention the angle, hight given than use tangent ratio in the right…

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

A:

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

A: Given: dxdt=5 ft/secdθdt=?

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

A:

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 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: A triangle has two constant sides of length 6 ft and 2 ft. The angle between these two sides is…

A:

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

A: Using triangle find angle then find the rate of change of angle

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

A:

Q: Find the length of the arc on a circle of radius 10 feet intercepted by a 135° central angle.…

A: Given: radius r=10 feet and θ=135o

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away 4. Trom…

A: We have to find how fast is the angle between the top of the ladder and the wall changing when the…

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

A:

Q: A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft from the…

A: Explained below

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: find the rate at which the area is increasing

A: Given an isoscles triangle has a constant length of 4 ft. Angle Ø between these sides increases at…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.