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45. A cylindrical tank of radius R and length L lying horizontally as in Figure 21 is filled with oil to height h. (a) Show that the volume V (h) of oil in the tank is V (h) = L ( R? )-(-n cos – h)v/2hR – h² (b) Show that = 2L /h(2R – h). (c) Suppose that R = 1.5 m and L = 10 m and that the tank is filled at a constant rate of 0.6 m³/min. How fast is the height h increasing when h = 0.5? FIGURE 21 Oil in the tank has level h.

45. A cylindrical tank of radius R and length L lying horizontally as in Figure 21 is filled with oil to height h. (a) Show that the volume V (h) of oil in the tank is V (h) = L ( R? )-(-n cos – h)v/2hR – h² (b) Show that = 2L /h(2R – h). (c) Suppose that R = 1.5 m and L = 10 m and that the tank is filled at a constant rate of 0.6 m³/min. How fast is the height h increasing when h = 0.5? FIGURE 21 Oil in the tank has level h.

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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45. A cylindrical tank of radius R and length L lying horizontally as in Figure 21 is filled with oil to height h. (a) Show that the volume V (h) of oil in the tank is V (h) = L ( R? )-(-n cos – h)v/2hR – h² (b) Show that = 2L /h(2R – h). (c) Suppose that R = 1.5 m and L = 10 m and that the tank is filled at a constant rate of 0.6 m³/min. How fast is the height h increasing when h = 0.5?
Transcribed Image Text:45. A cylindrical tank of radius R and length L lying horizontally as in Figure 21 is filled with oil to height h. (a) Show that the volume V (h) of oil in the tank is V (h) = L ( R? )-(-n cos – h)v/2hR – h² (b) Show that = 2L /h(2R – h). (c) Suppose that R = 1.5 m and L = 10 m and that the tank is filled at a constant rate of 0.6 m³/min. How fast is the height h increasing when h = 0.5?
FIGURE 21 Oil in the tank has level h.
Transcribed Image Text:FIGURE 21 Oil in the tank has level h.
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