(1 point) Susan finds an alien artifact in the desert, where there are temperatu
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(1 point) Susan finds an alien artifact in the desert, where there are temperature variations from a low in the 30s at night to a high in the 100s in the day. She is interested in how the artifact will respond to faster variations in temperature, so she kidnaps the artifact, takes it back to her lab (hotly pursued by the military police who patrol Area 51), and sticks it in an "oven" -- that is, a closed box whose temperature she can control precisely Let T(t) be the temperature of the artifact. Newton's law of cooling says that T(t) changes at a rate proportional to the difference between the temperature of the environment and the temperature of the artifact. This says that there is a constant k, not dependent on time, such that Tk(E - T), where is the temperature of the environment (the oven). Before collecting the artifact from the desert, Susan measured its temperature at a couple of times, and she has determined that for the alien artifact, k 0.55 Susan pre heats her oven to 90 degrees Fahrenheit she has stubborn y re used to join the metric world At time 0 the ove s at exactl , degrees and oven runs through a temperature cycle every 2 minutes, In which its temperature varies by 2 degrees above and 25 de rees below de ees. heating up, and the Let E(t) be the temperature of the oven after t minutes. Et)90+25sin(t) At time t = 0, when the artifact is at a temperature of 80 degrees, she puts it in the oven. Let T(t) be the temperature of the artifact at time t. Then T(0) = (degrees) 80 Write a differential equation which models the temperature of the artifact. T' = f(t,T) = Note: Use T rather than T) since the latter confuses the computer. Don't enter units for this equation. Solve the differential equation. To do this, you may find it helpful to know that if a is a constant, then 0.55(90+25sint-T) sin(t)eardt -e" (a sin(t)-cos(t)) + C. a2 +1 T() = 90+1 0.56(0.55sin(t)-cos(t))+0.56e^(-0.550 After Susan puts in the artifact in the oven, the military police break in and take her away. Think about what happens to her artifact as t-co and fill in the following sentence: For large values of t, even though the oven temperature varies between 65 and 115 degrees, the artifact varies from 76.25 to 103.75 degreesExplanation / Answer
I think there is some caculation mistake
90 + 10.56 ( 0.55^2 + 1^2 )^0.5 = 102.05
& 90 - 10.56 (0.55^2 + 1^2)^0.5 = 77.94
thats the correct answer
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