= 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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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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. =
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