A pie is removed from a refrigerator and thawed to 10 °C before being placed in an ovenpreheated at 200 °C. Assuming Newton's law of heating, the temperature T of the pdegrees Celsius °C. is described by the differential equationie, indT= -k(T -T),-k(T –dtwhere t is measured in minutes, k 0.02 /minute, and T is the surrounding temperature.How long (to the nearest minute) does it take for the pie to reach 6 times its initialtemperature? (Write down a numerical answer.)

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Answered: A pie is removed from a refrigerator…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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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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