An ice cube is freezing in such a way that the side length s, in inches, is s(t)=1/2t + 4 where t is in hours. The surface area of the ice cube is the function A(s) = 6s2. Part A: Write an equation that gives the volume at t hours after freezing begins. Part B: Find the surface area as a function of time, using composition, and determine its range. Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations, and check for extraneous solutions.
An ice cube is freezing in such a way that the side length s, in inches, is s(t)=1/2t + 4 where t is in hours. The surface area of the ice cube is the function A(s) = 6s2. Part A: Write an equation that gives the volume at t hours after freezing begins. Part B: Find the surface area as a function of time, using composition, and determine its range. Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations, and check for extraneous solutions.
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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An ice cube is freezing in such a way that the side length s, in inches, is s(t)=1/2t + 4 where t is in hours. The surface area of the ice cube is the function A(s) = 6s2.
Part A: Write an equation that gives the volume at t hours after freezing begins.
Part B: Find the surface area as a function of time, using composition, and determine its range.
Part C: After how many hours will the surface area equal 294 square inches? Show all necessary calculations, and check for extraneous solutions.
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