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13 Nov 2019
(3 points) 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. Suppose t is time, T is the temperature of the object, and Ts is the surrounding temperature The following differential equation describes Newton's Law dT ã¼=k(T-Ts), dt where k is a constant Suppose that we consider a 95° C cup of coffee in a 20° C room. Suppose it is known that the coffee cools at a rate of 1° C/min. when it is 70° C. Answer the following questions 1. Find the constant k in the differential equation Answer (in per minute): k- 1/25 2. What is the limiting value of the temperature? Answer (in Celsius): T- 95 3. Use Euler's method with step size h- 2 minutes to estimate the temperature of the coffee after 10 minutes Answer (in Celsius): T(10) ~
(3 points) 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. Suppose t is time, T is the temperature of the object, and Ts is the surrounding temperature The following differential equation describes Newton's Law dT ã¼=k(T-Ts), dt where k is a constant Suppose that we consider a 95° C cup of coffee in a 20° C room. Suppose it is known that the coffee cools at a rate of 1° C/min. when it is 70° C. Answer the following questions 1. Find the constant k in the differential equation Answer (in per minute): k- 1/25 2. What is the limiting value of the temperature? Answer (in Celsius): T- 95 3. Use Euler's method with step size h- 2 minutes to estimate the temperature of the coffee after 10 minutes Answer (in Celsius): T(10) ~
Patrina SchowalterLv2
7 Aug 2019