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garri49 [273]
3 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]3 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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Step-by-step explanation:

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LekaFEV [45]

Answer: one solution

Step-by-step explanation:

CONCEPT:

- One solution is when the final variable would be able to find a solution.

- Infinite solution is when the equations result in 0=0, meaning any number will fit

- No solution is when the equation results in both sides on equal.

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Given

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Expand Parenthesis

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Multiply both sides by the LCM of fractions (Least Common Multiple)

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Add both sides by 28

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Since we are able to get exactly one solution, there is only one solution.

Hope this helps!! :)

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