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Answer :
Final answer:
The differential equation for the temperature of the liquid is dT/dt = r(T - T_oven).
Explanation:
To write a differential equation for the temperature t(t) of the liquid, we can use the given information. The temperature of the liquid increases at a rate r times the difference between the temperature of the liquid and that of the oven. Let's denote the temperature of the liquid as T and the temperature of the oven as Toven. The differential equation can be written as dT/dt = r(T - Toven).
If T denotes the temperature of the liquid, and A the oven temperature, and r the rate constant, the mathematical representation of this idea is given by the differential equation: dT/dt = r*(A - T). This equation is based on Newton’s law of cooling and similar principles can also be applied in other disciplines such as chemistry and physics.
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