18 p please help me!

Mathematics

1 answer:

nevsk [136]3 years ago

7 0

It should be the second one

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Using Newton's Law of Cooling. You are a medical examiner called to an abandoned house in which a dead body has been discovered.

Artyom0805 [142]

A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
$\frac{dT}{dt} = \alpha(T -52)$

B) Find general solution by separating variables and integrating $\int\frac{dT}{T-52} = \alpha \int dt \\ ln (T-52) = \alpha t + C \\ T = C e^{\alpha t} +52$ :

C) Initial condition is t=0, T = 87
$87 = C +52 \\ C = 35$

D) Total time elapsed is 10 minutes, new temperature is 84
$84 = 35 e^{10\alpha} +52$
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E) Temperature function is:
$T = 35 e^{-.00896 t} +52$
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Plug in T = 98.6
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This is approximately 32 minutes before he arrived or about 1:20 AM

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3 years ago