MATHEMATICS HIGH SCHOOL

A cup of coffee at 181 degrees is poured into a mug and left in a room at 66 degrees. After 6 minutes, the coffee is 139 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T-66).1) What is the temperature of the coffee after 16 minutes?
2) After how many minutes will the coffee be 100 degrees?

Answers

Answer 1

Answer:

The temperature of the coffee after 16 minutes is 134 degrees and after 1.3 minutes the coffee be 100 degrees.

What is Differential equation?

A differential equation is an equation that contains one or more functions with its derivatives.

A cup of coffee at 181 degrees is poured into a mug and left in a room at 66 degrees.

After 6 minutes, the coffee is 139 degrees.

Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T-66).

T=∫k(t-66)dt

=k(t²/2-66)+c

When t=0 and T=181

181=k(0-66)+c

181=-66k+c

when t=6, T=139

139=k(6²/2-66)+c

139=-48k+c

-42=-18k

Divide both sides by 18

k=7/3

139=-48×7/3+c

c=139+112=251

T=7/3(t-66)+251

The temperature of the coffee after 16 minutes

T=7/3(16-66)+251

T=7/3(-50)+251

T=134 degrees

After how many minutes will the coffee be 100 degrees

100=7/3(t-66)+251

100=7/3t-7/3(66)+251

100=7/3t-154+251

100=7/3t+97

100-97=7/3t

3=7/3t

9/7=t

1.3=t

Hence, the temperature of the coffee after 16 minutes is 134 degrees and after 1.3 minutes the coffee be 100 degrees.

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Answer 2

Answer:

Answer:

Step-by-step explanation:

$(dT)/(dt) =k(t-66)\nT=\int\ {k(t-66)} \, dt=K((t^2)/(2) -66)+c\nwhen t=0,T=181\n181=K(0-66)+c\n181=-66k+c\nwhen t=6,T=139\n139=k((6^2)/(2) -66)+c\n139=-48k+c\n181-139=-66k+48k\n-42=-18k\n7=3k\nk=(7)/(3) \n139=-48*(7)/(3) +c\nc=139+112=251\nT=(7)/(3) (t-66)+251\nnow complete the question$

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Answers

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

♥☺

Ralph spends 15 1/3 hours per month playing tennis. How many hours does he play tennis in a year? (There are twelve months in a year.)a. 182 2/3
b. 164
c. 184
d. 164 1/3

Answers

Number of hours that Ralph spends playing tennis in a month = 15 1/3 hours
      = 46/3 hours
Number of months in a year = 12 months
Then
The total number of hours that Ralph spends playing tennis = (46/3) * 12 hours
      = 46 * 4 hours
   = 184 hours
So from the above deduction we can see that the total time spent by Ralph in playing tennis in a year is 184 hours. So the correct option among all the options given in the question is option "c". I hope the procedure is clear enough for you to understand.

184 hours a year cause 15x12 is 180hours and 20x 12 is 240 minutes and 240 minutes is 4 hours so 180+4 is 184 hours

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