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4 years ago

Sympilfy 31/-8...........

Mathematics

2 answers:

ArbitrLikvidat [17]4 years ago

8 0

Answer:

The fraction -31/8 cannot be simplified.

stiv31 [10]4 years ago

7 0

the answer is at the bottom circled.

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Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |

dsp73

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

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

$f_y=2y-x^2=0\implies2y=x^2$

If $x=0$ , then $y=0$ - critical point at (0, 0).
If $y=1$ , then $x=\pm\sqrt2$ - two critical points at $(-\sqrt2,1)$ and $(\sqrt2,1)$

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 $f(0,0)=7$ .

Now consider each boundary:

If $x=1$ , then

$f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4$

which has 3 extreme values over the interval $-1\le y\le1$ of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

If $x=-1$ , then

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

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

If $y=1$ , then

$f(x,1)=8$

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

If $y=-1$ , then

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

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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3 years ago

Six tubs for 12 piano lessons find the unit rate

V125BC [204]

12 / 6

Therefore the answer is 2

Hope this helped you today,

Have a good dayN

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3 years ago

ANSWER ASAP RIGHT ANSWER = BRAINLIST 100 POINTS

ale4655 [162]

Answer:

-6.75

Hooe it helps!

Please mark brainliest

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3 years ago

Read 2 more answers

45x^4 + 72x^3 is factored form

Rudik [331]

Answer: 9 x 3 ( 5 x + 8 )

Step-by-step explanation:

Factor 9 x 3 out of 45 x 4 + 72x 3 .

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3 years ago

A.) SSS B.) AAS C.) ASA D.) SAS

Vlada [557]

Side BC is congruent to side BC.

Using the congruent angles and the angle bisectors, you can get two angles congruent to two other angles, so you use ASA to prove the triangles congruent. Then you use CPCTC to prove the sides congruent.

Answer: C.) ASA

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4 years ago