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15. The radius r and height h of a circular cone change at a rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20?

15. The radius r and height h of a circular cone change at a rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20?

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How do you solve problem 15? Thanks
10. GUA conical tank (as in Example 2) has height 8 m and radius 4 m at the base. Water flows in at a rate of 3 m³/min. Determine as a function of h, and provide a graph of this relationship. In Exercises 11-14, refer to a 5-m ladder sliding down a wall, as in Fig- ures 5 and 6. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. 11. Assume the bottom slides away from the wall at a rate of 0.8 m/s. Find the velocity of the top of the ladder at 1 = 2 s if the bottom is 1.5 m from the wall at f = 0 s. 12. Suppose that the top is sliding down the wall at a rate of 1.2 m/s. Cal- culate dx/dt when h = 3 m. 13. Suppose that h(0) = 4 and the top slides down the wall at a rate of 1.2 m/s. Calculate x and dx/dt at t = 2 s. 14. What is the relation between h and x at the moment when the top and bottom of the ladder move at the same speed? 15. The radius r and height h of a circular cone change at a rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20? 19. At a s altitude of (a) The plane an (b) Ho when th C 2 16. A road perpendicular to a highway leads to a farmhouse located 2 km away (Figure 9). An automobile travels past the farmhouse at a speed of 80 km/h. How fast is the distance between the automobile and the farm- house increasing when the automobile is 6 km past the intersection of the highway and the road? 80 km/h 20. In the ra chang 21. 4 k obs of 23 a 1
Transcribed Image Text:10. GUA conical tank (as in Example 2) has height 8 m and radius 4 m at the base. Water flows in at a rate of 3 m³/min. Determine as a function of h, and provide a graph of this relationship. In Exercises 11-14, refer to a 5-m ladder sliding down a wall, as in Fig- ures 5 and 6. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. 11. Assume the bottom slides away from the wall at a rate of 0.8 m/s. Find the velocity of the top of the ladder at 1 = 2 s if the bottom is 1.5 m from the wall at f = 0 s. 12. Suppose that the top is sliding down the wall at a rate of 1.2 m/s. Cal- culate dx/dt when h = 3 m. 13. Suppose that h(0) = 4 and the top slides down the wall at a rate of 1.2 m/s. Calculate x and dx/dt at t = 2 s. 14. What is the relation between h and x at the moment when the top and bottom of the ladder move at the same speed? 15. The radius r and height h of a circular cone change at a rate of 2 cm/s. How fast is the volume of the cone increasing when r = 10 and h = 20? 19. At a s altitude of (a) The plane an (b) Ho when th C 2 16. A road perpendicular to a highway leads to a farmhouse located 2 km away (Figure 9). An automobile travels past the farmhouse at a speed of 80 km/h. How fast is the distance between the automobile and the farm- house increasing when the automobile is 6 km past the intersection of the highway and the road? 80 km/h 20. In the ra chang 21. 4 k obs of 23 a 1
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