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Following Newton's law of cooling, a body cools from 75°C to 65°C in 5 minutes when the surrounding temperature is 25°C. What will the body's temperature be at the end of the next 5 minutes (in °C)?

1. 57 °C
2. 55 °C
3. 60 °C
4. 58.5 °C

Correct answer: 57 °C

Solution

First interval: 10/5 = k*(70 - 25) -> k = 2/45. Applying the same relation to the next interval gives (65 - T)/5 = (2/45)*((65 + T)/2 - 25), which solves to T = 57°C.

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