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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.

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.

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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Please answer a and b and show the full solution. thanks.

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 m per minute. Find the height and the volume of the prism at this instant.
Transcribed Image Text: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 m per minute. Find the height and the volume of the prism at this instant.
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