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Consider a right cone (pointed downwards) that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 7 ft. How fast (in ft/min) does the depth of the water change when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min? ft/min Find the rate (in ft²/min) at which the surface area of the water changes when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min. ft²/min

Consider a right cone (pointed downwards) that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 7 ft. How fast (in ft/min) does the depth of the water change when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min? ft/min Find the rate (in ft²/min) at which the surface area of the water changes when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min. ft²/min

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a right cone (pointed downwards) that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 7 ft. How fast (in ft/min) does the depth of the water change when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min? ft/min Find the rate (in ft²/min) at which the surface area of the water changes when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min. ft²/min
Transcribed Image Text:Consider a right cone (pointed downwards) that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 7 ft. How fast (in ft/min) does the depth of the water change when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min? ft/min Find the rate (in ft²/min) at which the surface area of the water changes when the water is 10 ft high if the cone leaks water at a rate of 10 ft³/min. ft²/min
A vertical cylinder is leaking water at a rate of 2 ft³/s. If the cylinder has a height of 19 ft and a radius of 2 ft, at what rate (in ft/s) is the height of the water changing when the height is 9 ft? ft/s
Transcribed Image Text:A vertical cylinder is leaking water at a rate of 2 ft³/s. If the cylinder has a height of 19 ft and a radius of 2 ft, at what rate (in ft/s) is the height of the water changing when the height is 9 ft? ft/s
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