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garri49 [273]
3 years ago
11

( THE SUM OF THE MEASURES OF THE ANGLES BELOW IS 180* ) I will give brainlst for whoever gets this right and fills it out

Mathematics
1 answer:
Rufina [12.5K]3 years ago
5 0

Answer:

2x-10+x+x+10=180, or 4x=180

Step-by-step explanation:

So since the total is 180, you add them all up like an equation.

So,

2x-10+x+x+10

Combine like terms

4x=180

x=45

Then plug it back in to the equations.

x=45

(2x-10)=80

(x+10)=55

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Looks like f(x,y)=x^2+y^2-x^2y+7.

f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1

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The latter two critical points occur outside of D since |\pm\sqrt2|>1 so we ignore those points.

The Hessian matrix for this function is

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}

The value of its determinant at (0, 0) is \det H(0,0)=4>0, which means a minimum occurs at the point, and we have f(0,0)=7.

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f(-1,y)=8-y+y^2

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f(x,1)=8

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

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f(x,-1)=2x^2+8

which has 3 extreme values, but the previous cases already include them.

Hence f(x,y) has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

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