The length {, width w, and height h of a box change with time. At a certain instant the dimensions are l = 6 m and w = h = 1 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 4 m/s. At that instant find the rates at which the following quantities are changing. (a) the volume (in m m³/s) m³/s (b) the surface area (in m²/s) m2/s (c) the length of a diagonal (in m/s) (Round your answer to two decimal places.) m/s

Calculus: Early Transcendentals
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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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The length {, width w, and height h of a box change with time. At a certain instant the dimensions are l = 6 m and w = h = 1 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a
rate of 4 m/s. At that instant find the rates at which the following quantities are changing.
(a) the volume (in m
m³/s)
m³/s
(b) the surface area (in m²/s)
m2/s
(c) the length of a diagonal (in m/s) (Round your answer to two decimal places.)
m/s
Transcribed Image Text:The length {, width w, and height h of a box change with time. At a certain instant the dimensions are l = 6 m and w = h = 1 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 4 m/s. At that instant find the rates at which the following quantities are changing. (a) the volume (in m m³/s) m³/s (b) the surface area (in m²/s) m2/s (c) the length of a diagonal (in m/s) (Round your answer to two decimal places.) m/s
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