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A lake is fed by a stream with a constant flow rate of 1000 ft³/s. Water evaporates at a constant rate of 10 ft³/s per square mile of surface area. The surface area of the lake, Asurface, varies with h (in ft) according to the equation Asurface = 4 mi² +5(mi² / ft) · h : Assuming there is no drainage from the lake, determine: a) the rate of change of the volume in the lake if the depth is 19ft b) the steady-state depth of water in the lake

A lake is fed by a stream with a constant flow rate of 1000 ft³/s. Water evaporates at a constant rate of 10 ft³/s per square mile of surface area. The surface area of the lake, Asurface, varies with h (in ft) according to the equation Asurface = 4 mi² +5(mi² / ft) · h : Assuming there is no drainage from the lake, determine: a) the rate of change of the volume in the lake if the depth is 19ft b) the steady-state depth of water in the lake

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Problem 6.1 A lake is fed by a stream with a constant flow rate of 1000 ft³/s. Water evaporates at a constant rate of 10 ft³/s per square mile of surface area. The surface area of the lake, Asurface, varies with h (in ft) according to the equation Asurface = 4 mi² +5(mi² / ft) · h Assuming there is no drainage from the lake, determine: a) the rate of change of the volume in the lake if the depth is 19ft b) the steady-state depth of water in the lake Answers: (a) 8 ft³/sec <dv/dt < 12 ft³/sec; (b) 18 ft <h < 20 ft
Transcribed Image Text:Problem 6.1 A lake is fed by a stream with a constant flow rate of 1000 ft³/s. Water evaporates at a constant rate of 10 ft³/s per square mile of surface area. The surface area of the lake, Asurface, varies with h (in ft) according to the equation Asurface = 4 mi² +5(mi² / ft) · h Assuming there is no drainage from the lake, determine: a) the rate of change of the volume in the lake if the depth is 19ft b) the steady-state depth of water in the lake Answers: (a) 8 ft³/sec <dv/dt < 12 ft³/sec; (b) 18 ft <h < 20 ft
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