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3 years ago

ANSWERS plZ plZ plZ plZ plZ plZ

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

7 0

Answer: the page wont load all the way

Step-by-step explanation: she gonna need a lot of paint tho

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25 7 x 5 is 35

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In a murder investigation, the temperature of a corpse was 32.5 degrees C at 1:30 pm and 30.3 degrees C an hour later. Normal bo

svp [43]

Let $T(t)$ be the temperature of the body $t$ hours after 1:30 PM. Then $T(0) = 32.5$ and $T(1) = 30.3$ .

Using Newton's Law of Cooling, $\dfrac{dT}{dt} = k(T - T_s)$ , we have $\dfrac{dT}{dt} = k(T-20)$ . Now let $y = T - 20$ , so
$y(0) = T(0) - 20 = 32.5 - 20 = 12.5$ , so $y$ is a solution to the initial value problem $dy/dt = ky$ with $y(0) = 12.5$ .
By separating and integrating, we have $y(t) = y(0)e^{kt} = 12.5e^{kt}$ .

$y(1) = 30.3 - 20\ \Rightarrow\ 12.5e^{k(1)} = e^{k} = \frac{10.3}{12.5}\ \Rightarrow \\
k = \ln \frac{10.3}{12.5}
$

$y(t) = 37 - 20\ \Rightarrow\ 12.5e^{kt} = 17\ \Rightarrow\ e^{kt} = \frac{10.3}{12.5} \ \Rightarrow \\ \\
kt = \ln \frac{10.3}{12.5}\ \Rightarrow\ t = \left( \ln \frac{17}{12.5} \right)/ \frac{10.3}{12.5} \approx -1.588 \mathrm{\ h}$

≈ 95 minutes. Thus the murder took place about 95 minutes before 1:30 PM, or 11:55 AM.

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3 years ago