The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2), given in Section 3.1, is dT dt = KS(T-Tm), where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 155° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 105° F. If Tm = 75° F, then what is the temperature of the coffee in cup B after 30 min? (Round your answer to two decimal places.) OF

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
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2)
The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2),
given in Section 3.1, is
dT
dt
= KS(T-Tm),
where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the
temperature of the coffee is 155° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee
in cup A. After 30 min the temperature of the coffee in cup A is 105° F. If Tm = 75° F, then what is the temperature of the
coffee in cup B after 30 min? (Round your answer to two decimal places.)
OF
Transcribed Image Text:2) The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2), given in Section 3.1, is dT dt = KS(T-Tm), where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 155° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 105° F. If Tm = 75° F, then what is the temperature of the coffee in cup B after 30 min? (Round your answer to two decimal places.) OF
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