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= 4. The lengths a, b, c of the edges of a rectangular box are changing with time. At the instant in question, we know that a = 1 m, b = 2 m, c = 3 m, da/dt = db/dt = = 1 m/hr, and de/dt = -3 m/hr. At what rates are the box's volume V abc, surface area -S=2(ab+ac+bc), and internal diagonal D = √a² +62 + c² changing at that instant? One more time, start each of these three problems by sketching the corresponding tree diagram and don't forget units with your answers.

= 4. The lengths a, b, c of the edges of a rectangular box are changing with time. At the instant in question, we know that a = 1 m, b = 2 m, c = 3 m, da/dt = db/dt = = 1 m/hr, and de/dt = -3 m/hr. At what rates are the box's volume V abc, surface area -S=2(ab+ac+bc), and internal diagonal D = √a² +62 + c² changing at that instant? One more time, start each of these three problems by sketching the corresponding tree diagram and don't forget units with your answers.

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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4. The lengths a, b, c of the edges of a rectangular box are changing with time. At the instant in question, we know that a = 1 m, b = 2 m, c = = 3 m, da/dt = db/dt = 1 m/hr, and dc/dt -3 m/hr. At what rates are the box's volume V = abc, surface area S = 2(ab+ac+bc), and internal diagonal D = √a² +6² + c² changing at that instant? One more time, start each of these three problems by sketching the corresponding tree diagram and don't forget units with your answers. =
Transcribed Image Text:4. The lengths a, b, c of the edges of a rectangular box are changing with time. At the instant in question, we know that a = 1 m, b = 2 m, c = = 3 m, da/dt = db/dt = 1 m/hr, and dc/dt -3 m/hr. At what rates are the box's volume V = abc, surface area S = 2(ab+ac+bc), and internal diagonal D = √a² +6² + c² changing at that instant? One more time, start each of these three problems by sketching the corresponding tree diagram and don't forget units with your answers. =
Expert Solution
Step 1

Given,

a=1 m,b=2 m, c=3 m

da/dt=db/dt=1 m/hrdc/dt=-3 m/hr

To find the rates of changing volumeV=abc, surface areaS=2(ab+ac+bc) , and internal diagonal

D=a2+b2+c2 at that instant.

steps

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