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3 years ago

Which description is paired with its correct expression?

Mathematics

1 answer:

a_sh-v [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Hi there! You’re correct.

Twice the difference of nine and a number squared would look like

$2(9-n^2)$

I hope this helped! :)

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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).

3 0

3 years ago

The island has 600 bikes and 900 people. What is the bike to person ratio

jasenka [17]

Answer:

2:3 (2 bikes for every 3 people)

Step-by-step explanation:

hope this helps

8 0

2 years ago

I need help with this please. It’s probability.

Vinvika [58]

Answer:

2/13

Step-by-step explanation:

In a deck of 52 cards, there are 2 sets of red cards. Diamonds and Hearts. In each set of red cards, there are 4 fives. If there are 2 sets, that means that there are 8 red fives in the deck of 52 cards. This means that the probability is 8/52 which is simplified into 2/13.

8 0

3 years ago

Help Asap plz!!!! Thx Give 2<br>0 points

Arisa [49]

Answer:

(1,2) is a solution to both equations

Step-by-step explanation:

To determine if (1,2) is a solution to both equations, substitute into the equation and see if it is true

2x+y =4

2(1) + 2 =4

2+2 =4

4=4

true

y =3x-1

2 = 3(1) -1

2 =3-1

2=2

true

Since both statements are true

(1,2) is a solution to both equations

4 0

3 years ago

Will mark brainliest

Angelina_Jolie [31]

Answer:

K (-1,-1)

Step-by-step explanation:

4 0

2 years ago