Mathematics: Athermometer is taken from an inside room to the outside, where the air temperature is 20° f. after 1 minute the thermometer reads 70° f, and after 5 minutes it reads 45° f. what is the initial temperature of the inside room

Athermometer is taken from an inside room to the

Ответ:

lexijeppesen4533

13.03.2022

Mathematics

Using the Newton's law of cooling principle, the initial temperature of the inside room would be 79.44°F

According to the Newton's Law of Cooling :

$T(t) = T_{s} + (T_{o} - T_{s})e^{-kt}$ Temperature at a given time, t = 5 minutes = 45°

The equation can be expressed thus :

$\deltaT (T_{o} - T_{s})e^{-kt}$

$70 - 20 = (T_{o} - 20)e^{-k}$

$70 - 45 = (T_{o} - 20)e^{-5k}$

$50 = (T_{o} - 20)e^{-k}$ - - - (1)

$25 = (T_{o} - 20)e^{-5k}$ - - - - (2)

Divide (1) and (2) - - -

$\frac{50}{25} = e^{-k + 5k}$

$\frac{50}{25} = e^{4kt}$

$2 = e^{4kt}$

Take the ln

In 2 = 4k

k = 0.173

The initial temperature is defined thus :

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

$T(o) = 20 + (70 - 20)e^{0.173(1)}$

$T(o) = 20 + (50 \times 1.1888) = 79.44°F$

Therefore, the initial temperature is 79.44°F

Learn more :link

0,0(0 оценок)

Ответ:

gggg5019

13.03.2022

Mathematics

The change in the temperature is proportional to the difference in temperatures. Let's call the initial temperature of the room and the thermometer E_0

and the current temperature E(t)

where

is the elapsed time in minutes. The outside temperature is 20 F.

Newton's Law of Cooling:

$E(t) - 20 = (E_0 - 20) e^{- k t}$

We're given $E(1)=70 \textrm{ and } E(5)=45$

$70-20 = (E_0 - 20) e^{-k}$

$45-20 =(E_0 - 20) e^{-5k}$

Dividing,

$\dfrac{50}{25}=e^{4k}$

$k = \dfrac 1 4 \ln 2$

Now,

$E(t) - 20 = (E_0 - 20) e^{- k t}$

$E_0 = 20 + (E(t) - 20)e^{k t}$

$E_0 = 20 + (E(1) - 20)e^{k}$

$E_0 = 20 + (70 - 20)e^{\ln 2/4}$

$E_0 = 20 + 50 \cdot 2^{1/4} \approx 79.46 \textrm{ degrees F}$

0,0(0 оценок)

Ответ:

morrisjillian23

10.07.2020

Mathematics

The answer to your question is cos 30° =

The cosine is a trigonometric function. The cosine of an angle is done by dividing the length of a side of a traingle adjacent to the acute angle by the length of the longest side or the hypotenuse. For a complete list of angles and measurements, see the figure attached.

0,0(0 оценок)

Athermometer is taken from an inside room to the outside, where the air temperature is 20° f. after 1 minute the thermometer reads 70° f, and after 5 minutes it reads 45° f. what is the initial temperature of the inside room

Ответ:

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question