Step-by-step explanation: Newton's Law of Cooling 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:

$\frac{dQ}{dt}=\alpha.A.(T_{s}-T)$

This differential equation solved, gives the solution:

$T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}$

where

$T_{s}$ is temperature of the environment

$T_{0}$ 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°:

$27=22+(28-22)e^{-1k}$

$5=6e^{-k}$

$e^{-k}=\frac{5}{6}$

$ln(e^{-k})=ln(0.834)$

k = 0.1823

Using the parameter, find estimate time:

$28=22+(37-22)e^{-0.1823t}$

$6=15e^{-0.1823t}$

$ln(e^{-0.1823t})=ln(0.4)$

0.1823t = 0.9163

$t=\frac{0.9163}{0.1823}$

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.

5 0

3 years ago

Find an equation of the line having the given slope and containing the given point. m=8 (-4,-3)

notsponge [240]

Answer:

$y=8x+29$

Step-by-step explanation:

Since we know the slope and a point, we can use the point-slope form.

The point-slope form is:

$y-y_1=m(x-x_1)$

Substitute 8 for m, and let (-4,-3) be x₁ and y₁, respectively. Thus:

$y-(-3)=8(x-(-4))$

Simplify:

$y+3=8(x+4)$

Distribute:

$y+3=8x+32$

Subtract 3 from both sides:

$y=8x+29$

And we're done!

7 0

3 years ago

SOMEONE PLEASE HELP!!! what is the value of x? A.15 B.25 C.30 D.35

Amiraneli [1.4K]

The answer is D, 35 degrees. The 35 degree angle and angle x are opposite interior angles and are therefore congruent in measure.

4 0

3 years ago

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