A boat sails directly toward a 150-meter skyscraper that stands on the edge of a harbor. The angle of elevation 0 to the building is the angle formed by lines from the horizon and the top of the building. a. Express 0 in terms of x. b. What is the rate of change of the angle of 150 m elevation de /dx when the boat is x = 500 mm from the building?

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A:

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: 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 building that is 225 feet tall casts a shadow of various lengths as the day goes by. An angle of…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: Given y be the height of the Ballon ,t be time and theta the angle between the line of sight and the…

Q: The rate of change of the area enclosed between the circle and the square is squa meters per hour.

A: First find difference in area between square and circle then differentiate wrt t

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

A: .

Q: A searchlight is trained on the side of a tall building. As the light rotates, the spot it…

A: NOTE: Refresh your page if you can't see any equations. . D=distance between ground level and the…

Q: 1. A 15-meter ladder is resting against a vertical wall. If the bottom of the ladder is being pushed…

A: given: A 15-meter ladder is resting against a vertical wall. the bottom of the ladder is being…

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 kite 100 ft above the ground moves horizontally at a speed of 5 ft/s. At what rate is the angle…

A: Let's solve given rate of change problem.

Q: 10. A ladder 15 m long leans against the wall. The ladder slides down the wall at a rate of 1.5 m/s.…

A: Here we use the property of right angle triangle.

Q: 20. A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the…

A: Given : A kite is 100 ft above the ground moves horizontally at a speed of  8 ft/s. To find : At…

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: The objective of the problem is to find the speed at which the balloon is rising at the given…

Q: 19. A 6 foot ladder is sliding down a vertical wall at a rate of 1 foot per second. What is the rate…

A:

Q: 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is…

A: a)   What is the rate of change of the height of the top of the​ ladder?     Let x be the base…

Q: The radius of a circle is decreasing at a rate of 3 cm/sec. At what rate is the area of the circle…

A: The radius of a circle is decreasing at a rate of 3 cm/sec. At what rate is the area of the circle…

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A:

Q: kite 100 ft above the ground moves horizontally at a speed of 2 ft/s. At what rate is the angle (in…

A:

Q: 10. A kite 50 ft high, with 90 f of cord out. If the kite is moving horizontally at 3 ft/ sec…

A: Given:                           Height of kite =50 ft       dxdt=3 ft/sec

Q: A building that is 210 feet tall casts a shadow of various lengths z as the day goes by. An angle of…

A: Here we have to find rate of change of angle of elevation. In this problem we require few formulae,…

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: A hot air balloon rising vertically is tracked by an observer located 3 km from the lift-off point.…

A: topic- application of derivatives

Q: A building that is 219 feet tall casts a shadow of various lengths x as the day goes by. An angle of…

A: Now differentiating with respect to x, we get

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A: Here we will find how fast is the balloon rising,

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: 5m/s. Find the rate at which the angle between the boat and the surface of the water is changing,…

A: Introduction: Let h be the hypotenuse of a right-angle triangle, p is the height of the triangle and…

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

A: Let The height of the elevator above the ground level = x m…

Q: 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is…

A:

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

A:

Q: A hot air balloon rising vertically is tracked by an observer located 6 km from the lift-off point.…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 5 km from the lift-off point.…

A: Given: x=5 km θ=π5 raddθdt=0.3 rad/min The person and the hot air balloon form a right triangle,…

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

A: Height of kite flying above the ground is 100 ft Horizontal speed of kite is 12 ft/s We have to find…

Q: Assume that an airplane is flying toward you at a constant height h = 1 mile and at a speed = -20…

A:

Q: Find the rate of change of area of the circle with respect to its radius, in ft2/ft, when the radius…

A: We have to find the rate of change of area of the circle with respect to its radius in ft2/ft. Also…

Q: A kite 100 ft above the ground moves horizontally at a speed of 11 ft/s. At what rate is the angle…

A: For the given scenario, a rough sketch is as follows:

Q: A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point.…

A: A Hot air balloon is rising vertically . Angle between observer's line of sight and ballon is pi/5.…

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: The area of a square is increasing at a rate of 16 centimeters squared per second. Find the rate of…

A: Area of square =(side)2

Q: A rectangular beam is to be cut from a cylindrical log of diameter 20cm. Express the cross sectional…

A: It is given that the rectangular beam is cut from a cylindrical log of diameter 20cm.Therefore,…

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 hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Given that a hot air balloon is rising vertically is tracked by an observer located 7km from the…

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: Rate of change

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

A:

Q: D. Diego walks at the rate of 5 ft per second toward a street light whose lamp is 20 ft above the…

A:

Q: A hot air balloon rising vertically is tracked by an observer located 8 km from the lift-off point.…

A: From the given information we use trig ratio ,  tan(θ)=oppositeadjacent…

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.