21. A hot air balloon rising vertically is tracked by an observer located 4 km from the lift-off point. At a certain moment, the angle between the observer's line of sight and the horizontal is , and it is changing at a rate of 0.2 rad/min. How fast is the balloon rising at this moment?

Q: 4. A baseball diamond is a square 90 ft on a side. A player runs from first base to second base 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: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

Q: 1. A paper cup has the shape of a cone with height 12 cm and radius 4 cm (at the top). If water is…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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: 11. If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 2. A balloon in the shape of a sphere is being inflated at the rate of 100 cm/sec. a. At what rate…

A: a)  Given that the balloon is in the shape of sphere and it is being inflated at the rate of…

Q: 1. A boy is blowing a spherical balloon at a rate of 50 cm /s. At what rate is the radius of the…

A: This question is based on application of derivative.

Q: 1. A ladder 8 m long is leaning against a wall. If the bottom of the ladder is pulled horizontally…

A: We will draw figure and use differentiation  to find rate of change . Note . Only one question…

Q: A 5-ft-tall person walks toward a wall at a rate of 2 ft/sec. A spotlight is located on the ground…

A: 12. Let h be the height of shadow on wall using the similarity bof thr triangle,∆OAB, △OPQ,h40=540-x…

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: 1. The sides of a square decrease in length at rate 2 m/sec. At what rate is the area of the square…

A:

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: 1. Water is poured into a conical tank 6 m across the top and 8m deep at the rate of 10 How fast is…

A: To find: The rate of water level rising when water in the tank is 5 m deep. Formula used: The volume…

Q: and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this mom

A:

Q: 3. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a…

A: As per our guideline we are supposed to be answer only one question you can repost other question in…

Q: 1) A baseball diamond is a square whose sides are 90ft long. Suppose that a player running from…

A: Given : Side of Baseball diamond square =90 ft. Drawing the diagram of the whole situation,

Q: 2. A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall…

A:

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

A:

Q: 4. A spotlight is on the ground 20 feet away from a wall and a 6-ft tall person is walking towards…

A: Spot light and the wall is at the distance 20 ft.  Person height is 6 ft. He is walking towards the…

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

A:

Q: 9. A ladder 10ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A:

Q: 17. A man of height 1.8 m walks away from a 5-m lamppost at a speed of 1.2 m/s (Figure 9). Find the…

A:

Q: 2. a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down the…

A: Given:-  a) A ladder 10 ft long leans against a vertical wall. If the top of the ladder slides down…

Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

Q: 12. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 20…

A:

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Area of square = a2 Where a is length of side of square.

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: 18. Two cars start moving from the same point. One travels south at 60 mi/h and the other travels…

A:

Q: A 25 ft ladder is leaning against a vertical wall. 25 ft At what rate (with respect to time) is the…

A:

Q: 1. A conical paper cup 4 inches across the top and 4 inches deep is full of water. Since there is a…

A: We have been given the cone as in the figure  By the given figure we get r = 2 in. and h = 4 in. We…

Q: 9. If the volume and radius of a sphere are functions of time,what is the relationship between the…

A:

Q: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

A:

Q: 1.) Water is pouring into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top.…

A: step by step clear explanation is given .Have a look

Q: udent is walk

A: Here it is given that,  A student is walking towards the foot of a flagpole 20 meters high at the…

Q: A light is on the top of a 12 ft tall pole and a 5 ft 6 in tall person is waking away from the pole…

A: Given that:Height of the poll is 12 ft and height of the person is 5 ft 6 in or 5.5 ft.Let x and y…

Q: 33. The base x of the right triangle in Figure 14 increases at a rate of 5 cm/s, while the height…

A:

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

A:

Q: 18. A light is on the top of a 4-meter tall pole and a 1.5-meter tall person is walking away from…

A:

Q: 20. A 13 foot ladder leans against a vertical wall. When the ladder is pulled away from the wall at…

A:

Q: A 13-foot ladder rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Let the horizontal distance of foot of ladder from the wall be x and vertical distance from top of…

Q: 19. A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is…

A: Given :Radius of thr ripple increasing by 2 feet per secondCircumference = 2πr

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off…

A:

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A:

Q: 2. A man 1.8 meter tall walks away from a lamp post 4 meter high at a speed of 1.5 m/s. How fast is…

A: We'll answer one question since the exact one hasn't specified. Please re-submit the question you…

Q: 2. A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

A:

Q: 5. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a…

A: Given query is to find the speed at which bottom of the ladder is sliding.

Q: 1 A 5 m ladder is leaning against a wall of a house. The bottom of the ladder is pulled away from…

A: Let the bottom of the ladder is x meters away from the wall and the top of ladder is at distance y…

Q: 4. A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm…

A: Given: 4) Question is wrong (Some values are missed) 5) dxdt=10 ft/sec, h=100 ft, and l=125 ft