A lighthouse stands 475 m off a straight shore and the focused beam of its light revolves four times each minute. As shown in the​ figure, P is the point on shore closest to the lighthouse and Q is a point on the shore 200 m from P. What is the speed of the beam along the shore when it strikes the point​ Q? Describe how the speed of the beam along the shore varies with the distance between P and Q. Neglect the height of the lighthouse.

Q: Suppose the wheel of Dan’s bike is 70cm in diameter. It’s turning at a rate of 50 revolutions per…

A: In this question we have to find the linear speed in cm per minute.

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 street light is at the top of a 14 foot tall pole. A 6 foot tall woman walks away from the pole…

A:

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 mixing blade on a food processor extends out 3 inches from its center. If the blade is turning at…

A: Given that

Q: The horizontal and vertical components of the velocity of an arrow shot into the air are 16.1 feet…

A: To Determine: The horizontal and vertical components of the velocity of an arrow shot into the air…

Q: The horizontal and vertical components of the velocity of an arrow shot into the air are 16.1 feet…

A: Given data: The horizontal and vertical components are vx and vy respectively.

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

A:

Q: The carousel at Busch Gardens makes 3 revolutions per minute. What is the linear speed in feet per…

A: Given 3 revolutions per minute

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

A:

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

A:

Q: A beacon that makes one revolution every 7 seconds is located on a ship anchored 2 kilometers from a…

A: Find your answer below

Q: On a carousel, the outer row of animals is 20 feet from the center. The inner row of animals is 10…

A: Given  the outer row of animals is 20 feet from the centre The inner row of animals is 10 feet from…

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: It is height and distance problem.

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: Right triangle ABC has a hypotenuse BC that maintains a length of exactly 15 yards. If the leg AC is…

A: For finding the rate of change of angle  we will use some trigonometric functions like…

Q: An air traffic controller spots two airplanes at the same altitude converging to a point as they fly…

A: We sketch the situation roughly x=distance of the first plane from the origin y=distance of the…

Q: a light is placed on the ground at a distance of 31 feet from the point at which a javelin will be…

A: Distance between light and javelin is AB=31 feet,  At some moment, height of javelin is BC=28 feet…

Q: A mixing blade on a food processor extends out 2 inches from its center. If the blade is turning at…

A: This question can be solved using the concept of trigonometry.

Q: The figure below shows a camera mounted at a point 6000 ft from the base of a rocket launching pad.…

A:

Q: Tires of a bicycle have radius 30 inches and are turning at the rate of 2000 revolutions per hour.…

A: For a circle of radius r its circumference is given by 2πr. For a circle rolling on the ground in…

Q: the base of a right triangle is fixed at 3 ft., the hypotenuse is 5 ft long and subject to change.…

A: We have been given that the right triangle has a fixed base of 3ft. and the hypotenuse is 5 ft. long…

Q: Suppose you always keep your eyes fixed on the very top of a 100 m building. Suppose you start to…

A: Height of building = 100 m Let x be the base distance from the building Head angle = θ tanθ=100x

Q: A stone was dropped off a cliff and hit the ground with aspeed of 120 fts. What is the height of…

A: Initial velocity = 0 ft/s Final velocity= 120 ft/s Acceleration= a= 32.2 ft/s^2 Let the height = h…

Q: The base of a right triangle is fixed at 3 ft., the hypotenuse is 5 ft. Iong and subject to change.…

A: Pythagoras Theorem states that in right triangle the length of square of hypotenuse is equal to the…

Q: A carousel has a radius of 17 feet and takes 28 seconds to make one complete revolution. What is the…

A: Given that the radaius of circle (r)= 17 feettime taken to complete one revolution =28 secThe…

Q: The figure below shows a camera mounted at a point 3000 ft from the base of a rocket launching pad.…

A: Suppose, we name the sides as shown:

Q: What do we say if the truncation error if it is proportional to h?

A:

Q: Find the rate of change of the angle when a wire of 250 dx feet is attached.

A:

Q: A balloon leaves the ground 50 ft from an observer, rises at the rate of 8 ft/sec. How fast is the…

A:

Q: Find a linear speed of a tip of minute hand if a length of the minute hand is 28 cm long. Hint: ()…

A: We need to find linear speed of tip of a minute hand, if the length of the minute hand is 28cm. We…

Q: A tire of a Dogde car with a 22-inch diameter is turning at the rate of 35 revolutions per minute.…

A:

Q: You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 2…

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: The second hand on a clock completes one full revolution per minute. If that second h what it is…

A: Given that: Second hand completes one full revolution per minute.Length of second hand = 15cm

Q: A street light is at the top of a 10 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: A gasoline-driven lawnmower has a blade that extends out 1 foot from its center. The tip of the…

A:

Q: The figure below shows a camera mounted at a point 6000 ft from the base of a rocket launching pad.…

A:

Q: A baseball diamond is a square, 90 feet on the side. A runner runs from second base to the third…

A:

Q: Q3: You are videotaping a race from a stand 132 ft from the track, following a car that is moving at…

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: You are videotaping a race from a stand 132 ft from the track, following a car that is moving at 180…

A: To  Determine: How fast will your camera angle u be changing when the car is right in front of you?…

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 mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole…

A:

Q: OA man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 19 ft high. At what rate…

A:

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

A:

Q: The deck of a bridge is suspended 295 feet above a river. If a pebble falls off the side of the…

A: The deck of a bridge is suspended 295 feet above a river. If a pebble falls off the side of the…

Q: You are videotaping a race from a stand 132 ft. from the track, following a car that is moving at…

A:

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.