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soldi70 [24.7K]
4 years ago
10

The temperature T of a cup of coffee is a function T(t) where t is the time in minutes. The room temperature is 18° Celsius. The

rate at which the coffee cools down is proportional to the difference between the temperature of the coffee and the room temperature. Use this information to write a differential equation describing the derivative of the coffee temperature in terms of T and t. Use C as your proportionality constant. C should be a positive number. Write T instead of T(t).
Mathematics
1 answer:
ella [17]4 years ago
7 0

Answer:

(1/C)dR/dt - dT/dt = 0

Step-by-step explanation:

Let R be the rate at which the coffee cools down. Since R is proportional to the difference between the temperature of the coffee, T and the room temperature, we write

R = C(T - 18)

Where C is the proportionality constant.

To write a differential equation describing the derivative of the coffee temperature in terms of T and t, we need to differentiate

R = C(T - 18)

with respect to t.

Doing that, we have

dR/dt = CdT/dt

Or

(1/C)dR/dt - dT/dt = 0

Which is the required differential equation.

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Use FOIL to check answer



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A cellphone company charges a monthly rate of $1295 and $25 a minutes per call. the bill for x minutes is$212000. write a equati
Viktor [21]

The equation 25x+1295=212000 models the situation. The bill had charges of 8428.2 minutes

Step-by-step explanation:

Given,

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As x are the total minutes.

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Dividing both sides by 25

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The equation 25x+1295=212000 models the situation. The bill had charges of 8428.2 minutes

Keywords: division, subtraction

Learn more about division at:

  • brainly.com/question/106975
  • brainly.com/question/107042

#LearnwithBrainly

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