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3. A rectangular prism with dimensions 6 m x 4 m x 8 m (l x w x h) is shrinking. 8 m 4 m 6 m Answer the following items independent of each other. (a) Assume that the length and width remains constant, while the height of the prism is changing. When the height is decreasing at a rate of 2 m per minute, how fast is the volume of the prism changing? (b) Now, assume that the length, width, and height are changing, but their ratio is maintained. When the height is decreasing at a rate of 2 m per minute, the volume is decreasing at a rate of 36 m3 per minute. Find the height and the volume of the prism at this instant.

3. A rectangular prism with dimensions 6 m x 4 m x 8 m (l x w x h) is shrinking. 8 m 4 m 6 m Answer the following items independent of each other. (a) Assume that the length and width remains constant, while the height of the prism is changing. When the height is decreasing at a rate of 2 m per minute, how fast is the volume of the prism changing? (b) Now, assume that the length, width, and height are changing, but their ratio is maintained. When the height is decreasing at a rate of 2 m per minute, the volume is decreasing at a rate of 36 m3 per minute. Find the height and the volume of the prism at this instant.

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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3. A rectangular prism with dimensions 6 m x 4 m x 8 m (l x w x h) is shrinking. 8 m 4 m 6 m Answer the following items independent of each other. (a) Assume that the length and width remains constant, while the height of the prism is changing. When the height is decreasing at a rate of 2 m per minute, how fast is the volume of the prism changing? (b) Now, assume that the length, width, and height are changing, but their ratio is maintained. When the height is decreasing at a rate of 2 m per minute, the volume is decreasing at a rate of 36 m3 per minute. Find the height and the volume of the prism at this instant.
Transcribed Image Text:3. A rectangular prism with dimensions 6 m x 4 m x 8 m (l x w x h) is shrinking. 8 m 4 m 6 m Answer the following items independent of each other. (a) Assume that the length and width remains constant, while the height of the prism is changing. When the height is decreasing at a rate of 2 m per minute, how fast is the volume of the prism changing? (b) Now, assume that the length, width, and height are changing, but their ratio is maintained. When the height is decreasing at a rate of 2 m per minute, the volume is decreasing at a rate of 36 m3 per minute. Find the height and the volume of the prism at this instant.
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