Change each of the following decimals to a fraction. Reduce your answer to its lowest terms.

Mathematics

1 answer:

cluponka [151]3 years ago

8 0

7/100

3/10

21/125

3/ 2500

7/50

I simplified them for you

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A thermometer is taken from an inside room to the outside, where the air temperature is 20° f. after 1 minute the thermometer re

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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 $t$ 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,

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

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

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

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

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

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Round 1.24236 to the nearest hundredth

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Answer:

1.24

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