3. An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 miles per hour. Find the rate of change of the angle of elevation when the angle is 60 degrees.

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: An observer is 20 m above the ground floor of a large hotel atrium looking at a glass-enclosed…

A: Given, an observer is 20 m above the ground floor of a large hotel, The observer looking at 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. Let x be the distance between the bottom…

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: Find the rate of change. The diameter of a circle with respect to radius

A:

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

A: Given: A mixing blade on a food processor extends out 3 inches from its center. That is,…

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 man whose eye level is 6 ft above the ground walks toward a billboard at a rate of 2 ft>s. The…

A:

Q: When a rocket is 5 kilometers high, it is moving vertically upward at a speed of 900 kilometers per…

A:

Q: Two planes, at elevations differing by 144 meters, pass overhead, heading in opposite directions.…

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: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A:

Q: A certain escalator travels at a rate of 13.4 meters per minute, and its angle of inclination is…

A: So from the triangle we have: Answer(a): Vertical component of the velocity is 6.1667 meters per…

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 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

A:

Q: An engineering student is experimenting on a cylindrical can with a fixed rate of 8 inches. Find the…

A:

Q: A small rocket is launched straight up in the air at a speed of 4ft/sec. A camera on the ground, 10…

A: Consider the given information. At any time t, rocket is at C tanθ=ACAB=AC10

Q: MY When a rocket is 6 kilometers high, it is moving vertically upward at a speed of 600 kilometers…

A: Solve to the given question condition

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: Two boats leave a port at the same time: one travels west at 20 mi/hr and the other travels south at…

A:

Q: A 15-meter ladder is resting against a vertical wall, If the bottom of the ladder is being pushed…

A: Let ladder AB, l=15 m, Ladder is pushed horizontally at the rate of 1.5 m/s, ⇒dydt=1.5 We need to…

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 3 inches from its center. If the blade is turning at…

A: 1 foot  =  12 inches     1 inch  =  112 foot 3 inches  = 312 feet                 =  14 feet

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

A: Given : Length of the ladder = 20 ft

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: drive has a maximum speed of 12,000 revolutions per minute. If a disc has a diameter of 12 cm, what…

A: A drive has a maximum speed of 12,000 revolutions per minute. If a disc has a diameter of 12 cm,…

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 kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

A:

Q: The radius, r, of a circle is decreasing at a rate of 2 centimeters per minute.  Find the rate of…

A:

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

A: According to question Let x be the distance between lamp post and man at any instant of time "t"y…

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

A: l = length of ladder y = height of ladder from the ground x = distance moved away from the wall…

Q: An aircraft is climbing at a 300 angle to the horizontal. How fast is the aircraft gaining altitude…

A: An aircraft is climbing at a constant 30 degree angle to the horizontal and the speed is 500 mph…

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

A: We need to find rate of distance changing.   ddθ(cscθ)=-csc(θ)cot(θ)

Q: 49. A plane flying with a constant speed of 300 km/h passes over a ground radar station at an…

A: Form the triangle and use cousin formula then take the derivative.

Q: a. How fast is the top of the ladder sliding down the wall when the base of the ladder is 12 feet…

A: It is given that the length of ladder is 13 foot which acts as the hypotenuse of the right angled…

Q: A ladder 20 ft. long leans against a house. When it is 16 ft. from the house, find the rate at…

A:

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

A:

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

A:

Q: What is the rate of change of the area of a circle (A = pair2 ) with respect to the radius when the…

A: It is required to calculate the rate of change of area of circle with respect to radius when radius…

Q: A kite is flying 25 meters above the flat Earth and being blown by the wind in the horizontal…

A: To calculate rate of change of angle between kite and grounds.  Let theta is the angle between kite…

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: