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garri49 [273]
2 years ago
10

A liquid at temperature 7575F is placed in an oven at temperature 450450. The temperature of the liquid increases at a rate 77 t

imes the difference between the temperature of the liquid and that of the oven. Write a differential equation for the temperature T(t) of the liquid.
Mathematics
1 answer:
hichkok12 [17]2 years ago
5 0

Answer: \dfrac{dT(t)}{dt}=77\times (450-T)

Step-by-step explanation:

Given

The temperature of the liquid is 75^{\circ}F placed in an oven with temperature of 450^{\circ}F.

Initially difference in temperature of the two

\Delta T=450-75\\\Rightarrow \Delta T=375^{\circ}F

According to the question

\Rightarrow \dfrac{dT(t)}{dt}=77\cdot \Delta T\\\\\Rightarrow \dfrac{dT(t)}{dt}=77\times (450-T)\quad [\text{T=75}^{\circ}F\ \text{at t=0}]

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