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

Sagot :

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

Step-by-step explanation:

Given

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

Initially difference in temperature of the two

[tex]\Delta T=450-75\\\Rightarrow \Delta T=375^{\circ}F[/tex]

According to the question

[tex]\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}][/tex]

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