I am stuck on this math problem: Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature. In the book, I got the differential equation of Newton's Cooling which is dT/dt = k(A-T). T is the temperature, A is the ambient temperature, t is the time in minutes, k is a constant. By separating the variables and integrating both sides, I got T= A + e^c * e^kt. I tried to solve for A using the available values, but can't seem to solve for A.
I am stuck on this math problem: Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature. In the book, I got the differential equation of Newton's Cooling which is dT/dt = k(A-T). T is the temperature, A is the ambient temperature, t is the time in minutes, k is a constant. By separating the variables and integrating both sides, I got T= A + e^c * e^kt. I tried to solve for A using the available values, but can't seem to solve for A.
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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I am stuck on this math problem:
Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature.
In the book, I got the differential equation of Newton's Cooling which is dT/dt = k(A-T). T is the temperature, A is the ambient temperature, t is the time in minutes, k is a constant.
By separating the variables and integrating both sides, I got T= A + e^c * e^kt.
I tried to solve for A using the available values, but can't seem to solve for A.
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