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2 years ago

Can someone help me with this? (statistics) (Dot plot) you need to answer I,J,K, and L. Pls help ASAP

Mathematics

1 answer:

adell [148]2 years ago

4 0

Answer:

K is class A and L is 40%.

Step-by-step explanation:

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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

PLEASE HELP

ozzi

Hope this helps, I searched it up for you

6 0

1 year ago

Can I get another answer please ?

gavmur [86]

G(x) = x^2 + 2x + 6
g(x) = x^2 + 2x + 1 + 5
g(x) = (x+1)^2 + 5

so
f(x) = x^2 to g(x) = (x+1)^2 + 5
shifted to the left 1 unit and up 5 units

answer is A. left 1 unit and up 5 units

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3 years ago

A computer programmer's yearly income of $82,000 is increased by 6%. What is the dollar amount of the increase, and what is her

Vinvika [58]

The new yearly income is $86920.
Convert 6% into a decimal which is 0.06.
1ST METHOD:
82000*0.06=4290
4290+82000=86920
2ND METHOD:
0.06+1=1.06
82000*1.06=86920

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2 years ago

Read 2 more answers

What is the expression in the factored x2+7x+6

Sedbober [7]

Answer:

Step-by-step explanation:

x² +7x + 6 = (x+1)(x+6)

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2 years ago