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sergiy2304 [10]
3 years ago
8

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

dy temperature is 37.0 degrees C and the temperature of the surroundings was 20.0 degrees C. When did the murder take place?
Mathematics
1 answer:
svp [43]3 years ago
6 0
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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Ishaan is 222 times as old as Christopher. 353535 years ago, Ishaan was 777 times as old as Christopher.
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<h3><u>Question:</u></h3>

Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. How old is Christoper now?

<h3><u>Answer:</u></h3>

The present age of Christoper is 42 years old

<h3><u>Solution:</u></h3>

Given that Ishaan is 2 times as old as Christoper

Let the present age of Christoper be "x"

Then, Present age of Ishaan = 2 times as old as Christoper

present age of Ishaan = 2x

<em><u>35 years ago, Ishaan was 7 times as old as Christopher</u></em>

Age of Ishaan 35 years ago = Present age of Ishaan - 35

Age of Ishaan 35 years ago = 2x - 35

Similarly,

Age of christoper 35 years ago = Present age of christoper - 35

Age of christoper 35 years ago = x - 35

From given statement, 35 years ago, Ishaan was 7 times as old as Christopher

Age of Ishaan 35 years ago = 7 times the age of Christoper 35 years ago

(2x - 35) = 7(x - 35)

<em><u>Solve the above equation for "x"</u></em>

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Step-by-step explanation:

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But this is wrong because when bases are same exponents are added.

This is the law of exponents.

The correct form would be

2^3·2^2 = 2^3+2 = 2^5  

For understanding it better we can write it like this

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