Evaluate the expression when y=6 y²-9y-7
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Answer: Mr. Ratchett died approximately at 2AM.
Step-by-step explanation: <u>Newton's</u> <u>Law</u> <u>of</u> <u>Cooling</u> shows the cooling rate between a body and the environment, by stating that the rate is proportional to the difference in temperatures between them.
Mathematically, it is represented as:
This differential equation solved, gives the solution:
where
is temperature of the environment
is the initial temperature of the body
k is a parameter dependent of heat transfer coefficient, heat capacity and area of the body
t is time required to change the temperature
For the murder on the Orient Express, first determine parameter k.
In 1 hour, Mr. Ratchett's body decrease 1°:
k = 0.1823
Using the parameter, find estimate time:
0.1823t = 0.9163
t ≈ 5 hours
The body was found at 7AM. So, it took approximately 5 hours to cool down to 28° at that time. Therefore, Mr. Ratchett died at 2AM.