Suppose you have just poured a cup of freshly brewed coffee with temperature 93°C in a room where the temperature is 20ºC. (a) When do you think the coffee cools most quickly? What happens to the rate of cooling as time goes by? Explain. The coffee cools most quickly as soon as ---Select--- ✓. The rate of cooling ---Select--- towards ---Select--- since the coffee approaches room temperature. (b) Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Write a differential equation that expresses Newton's Law of Cooling for this particular situation. (Use t as the independent variable, y as the dependent variable, R as the room temperature, and k as a proportionality constant.) dy dt What is the initial condition? y(0) = In view of your answer to part (a), do you think this differential equation is an appropriate model for cooling? The answer and the model ---Select--- dy ✓ because as y approaches R, approaches ---Select--- dt so the model seems appropriate. (c) Make a rough sketch of the graph of the solution of the initial-value problem in part (b).

Suppose you have just poured a cup of freshly brewed coffee with temperature 93°C in a room where the temperature is 20ºC. (a) When do you think the coffee cools most quickly? What happens to the rate of cooling as time goes by? Explain. The coffee cools most quickly as soon as ---Select--- ✓. The rate of cooling ---Select--- towards ---Select--- since the coffee approaches room temperature. (b) Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Write a differential equation that expresses Newton's Law of Cooling for this particular situation. (Use t as the independent variable, y as the dependent variable, R as the room temperature, and k as a proportionality constant.) dy dt What is the initial condition? y(0) = In view of your answer to part (a), do you think this differential equation is an appropriate model for cooling? The answer and the model ---Select--- dy ✓ because as y approaches R, approaches ---Select--- dt so the model seems appropriate. (c) Make a rough sketch of the graph of the solution of the initial-value problem in part (b).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 16EQ

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