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jaqwannewsome
13.03.2021 •
Mathematics
A flat circular plate has the shape of the region x squared plus y squared less than or equals 1.The plate, including the boundary where x squared plus y squared equals 1,is heated so that the temperature at the point (x comma y )is Upper T (x comma y )equalsx squared plus 2 y squared minus three halves x.Find the temperatures at the hottest and coldest points on the plate.
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Ответ:
We have the coldest value of temperature
. and the hottest value is
.
Step-by-step explanation:
We need to take the derivative with respect of x and y, and equal to zero to find the local minimums.
The temperature equation is:
Let's take the partials derivatives.
So, we can find the critical point (x,y) of T(x,y).
The critical point is (3/4,0) so the temperature at this point is:![T(\frac{3}{4},0)=(\frac{3}{4})^{2}+2(0)^{2}-(\frac{3}{2})(\frac{3}{4})](/tpl/images/1193/0823/aada8.png)
Now, we need to evaluate the boundary condition.
We can solve this equation for y and evaluate this value in the temperature.
Now, let's find the critical point again, as we did above.
Evaluating T(x,y) at this point, we have:
Now, we can see that at point (3/4,0) we have the coldest value of temperature
. On the other hand, at the point
we have the hottest value of temperature, it is
.
I hope it helps you!
Ответ:
Bottom left corner
Step-by-step explanation:
This is because that the graph at the bottom has the dots scattered equally with one near the lone of best fit which means that it'll show better accuracy.
Hope this helps :)
Have a nice day!!!