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4 years ago

How to find the answers

Mathematics

1 answer:

Ksivusya [100]4 years ago

8 0

You should ask for help,Don't be embarrassed to ask.

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A flat circular plate has the shape of the region x squared plus y squared less than or equals 1.The plate, including the bound

rjkz [21]

Answer:

We have the coldest value of temperature $T(\frac{3}{4},0) = -9/16$ . and the hottest value is $T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$ .

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:

$T(x,y)=x^{2}+2y^{2}-\frac{3}{2}x$

Let's take the partials derivatives.

$T_{x}(x,y)=2x-\frac{3}{2}=0$

$T_{y}(x,y)=4y=0$

So, we can find the critical point (x,y) of T(x,y).

$2x-\frac{3}{2}=0$

$x=\frac{3}{4}$

$4y=0$

$y=0$

The critical point is (3/4,0) so the temperature at this point is: $T(\frac{3}{4},0)=(\frac{3}{4})^{2}+2(0)^{2}-(\frac{3}{2})(\frac{3}{4})$

$T(\frac{3}{4},0)=-\frac{9}{16}$

Now, we need to evaluate the boundary condition.

$x^{2}+y^{2}=1$

We can solve this equation for y and evaluate this value in the temperature.

$y=\pm \sqrt{1-x^{2}}$

$T(x,\sqrt{1-x^{2}})=x^{2}+2(1-x^{2})-\frac{3}{2}x$

$T(x,\sqrt{1-x^{2}})=-x^{2}-\frac{3}{2}x+2$

Now, let's find the critical point again, as we did above.

$T_{x}(x,\sqrt{1-x^{2}})=-2x-\frac{3}{2}=0$

$x=-\frac{3}{4}$

Evaluating T(x,y) at this point, we have:

$T(-(3/4),\sqrt{1-(-3/4)^{2}})=-(-\frac{3}{4})^{2}-\frac{3}{2}(-\frac{3}{4})+2$

$T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$

Now, we can see that at point (3/4,0) we have the coldest value of temperature $T(\frac{3}{4},0) = -9/16$ . On the other hand, at the point $-(3/4),\frac{\sqrt{7}}{4})$ we have the hottest value of temperature, it is $T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}$ .

I hope it helps you!

4 0

3 years ago

Brainliest and 20 points!!!!

denis23 [38]

Answer:

Step-by-step explanation:

The n th term ( explicit formula) for a geometric sequence is

f(n) = a $(r)^{n-1}$

where a is the first term and r the common ratio

Here a = 2 and r = - 8 ÷ 2 = - 4, thus

f(n) = 2 $(-4)^{n-1}$

6 0

4 years ago

Molly uses 192 beads to make a bracelet and a necklace. It takes 5 times as many beads to make a necklace than it does to make a

levacccp [35]

960 beads are used to make the necklace.

192 x 5 = 960, so that's how i got my answer and then you just divide to check if it's right or not.

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3 years ago

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Please help me with this math

victus00 [196]

Answer:

Step-by-step explanation:

These two angles are equal to each other

set the formulas equal to each other and solve

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3 years ago

Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the nu

Lelu [443]

Answer:

x = 44 − y

Step-by-step explanation:

x is the number of glasses of iced tea, and y is the number of glasses of lemonade. The sum is 44, so:

x + y = 44

Solving for x:

x = 44 − y

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3 years ago

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