- 5y + 12 = - 4(2y + 3)

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te

Aleonysh [2.5K]

Answer:

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

$\frac{dT}{dt}=-k(T-T_{s})$

T is temperature of a cup of coffee at any time t $T_{s}$ , is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

$T(0)=190\\T(1)=170\\T_{s}=66$

$\frac{dT}{dt}=-k(T-T_{s})\\\frac{dT}{(T-T_{s})}=-k*dt\\\int\limits {\frac{1}{T-T_{s} } } \, dT=-\int\limits {k} \, dt\\ln(T-T_{s})=k*t+C\\e*ln(T-T_{s})=e^{k*t+C} \\T-T_{s}=e^{k*t}*e^{C}\\e^{C}=C\\T-T_{s}=e^{k*t}*C\\T=T_{s}+e^{k*t}*C$

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

$T=T_{s} +e^{-k*t}*C\\ C=190-66=124\\170=66+124*e^{-k*2}\\ 170-66=124*e^{-k*2}\\ln(\frac{104}{124})=ln*e^{-k*2}\\-0.175=-k*2\\k=0.08794$

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

$145=66+124*e^{-k*t} \\145-66=124*^{-0.087*t}$

$ln(0.637)=ln*e(-0.087*t)\\-0.45=-0.087*t\\t=5.18minutes$

4 0

2 years ago

P = A + B + C Find P if A = 23 B = 17 C = 29 P=

madam [21]

Answer:

P = 69!

Step-by-step explanation:

23+17+29 = 69 :)

3 0

2 years ago

Read 2 more answers

What do you think Thomas Edison meant by the word perspiration? How do those words apply to what you've learned about businesses

EastWind [94]

1. Thomas Edison used "perspiration" to refer to the physical and mental efforts needed to achieve a meaningful purpose in any human endeavor.

2. As it applies to businesses, it is not enough to develop a business idea or plan, as the business person must be prepared to execute and carry the business idea or plan to fruition.

<h3>What does Thomas Edison's reference mean?</h3>

According to Thomas Edison, the superior intellect or creativity we associate with great minds comes from inspiration (the idea) and perspiration (hard work).

Perspiration literarily refers to the sweat that emanates as someone works hard.

Without a strong working ethic, it will be impossible to achieve great results from only the proposition of great ideas or business plans.

Learn more about Thomas Edison at brainly.com/question/26568016

5 0

1 year ago

PLZZZZ HELP ME!!!!! I WiLL MARK U AS BRAINLIEST

uranmaximum [27]

Answer:

Step-by-step explanation:

I would say you can distribute the money by saving $25 dollars for your medium and log term and $50 for your short term. Because you will eventually raise enough from your paycheck to get your laptop. Then, once you get your laptop you put more money to your other terms.

5 0

3 years ago

A number cube is rolled 350 times and these are the results: 60 ones, 65 twos, 54 threes, 63 fours, 62 fives, and 46 sixes. What

BlackZzzverrR [31]

The experimental probability can be represented as a fraction of the number of times a five was not the result over the total number of times the cube was rolled.

The answer would be 288/350 or 144/175.

7 0

2 years ago