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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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y=-3

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Putting the given value of 'x' in the equation:

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Write an equation in point-slope form of the line that passes through the point (2, -8) and has a slope of 4
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2 years ago
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is
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harina [27]
There is no greatest perimeter of a rectangle with an area of 39 square feet.

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Now consider length of 3/2 = 1.5 and 13·2 = 26. Then area is same but perimeter is 1.5 + 1.5 + 26 + 26 = 55.

Now we can just repeatedly half the length and double the width.

L = 3.0, W = 13
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L = 1.5, W = 26   
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L = 0.75, W = 52   
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L = 0.375, W = 104  
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L = 0.1875, W = 208  
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L = 0.09375, W = 416  
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L = 0.046875, W = 832  
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L = 0.0234375, W = 1664 
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L = 0.01171875, W = 3328 
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L = 0.005859375, W = 6656 
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 Notice how P just kept growing. That's because width grow much faster than length <span>shrinking, </span>so P would grow endlessly.

Hope this helps.
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