consider a 38 degree F object placed in 68 F room write a differential equation for T thetemperature of the object at time t using k>0 fo

Question

consider a 38 degree F object placed in 68 F room write a differential equation for T thetemperature of the object at time t using k>0 for the constant of proportionality and write your equation in terms of T k and t

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Kim Chi 3 years 2021-09-02T13:29:26+00:00 1 Answers 2 views 0

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  1. sori
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    2021-09-02T13:30:41+00:00
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    Answer:

    dY/dt = k(Y – Ys).

    Explanation:

    Okay, this question based on the law known as the Newton’s law of cooling. According to Newton’s law of cooling, when an object is placed into a specific or particular environment, the object’s temperature will definitely be lower than the temperature of the surrounding or the environment.

    So, we are given that the temperature of the object = 38 degree F = Y(o) of the object and the temperature of the environment = 68 degree F = Ys

    Hence, dY/dt = k(Y – Ys).

    dY/ (Y – Ys) =kdt.

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