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3 years ago

I REALLY NEED HELP ASAP

Mathematics

1 answer:

guapka [62]3 years ago

6 0

The Correct option is -4

because every other terms result in value = 4, where's -4 is the only different one hence doesn't belongs yo other three

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Lola saved $86.25 in 3 months. She saved $30.75 in the first month and $7.99 in the second month. How much money did Lola save i

pickupchik [31]

The correct answer is 47 dollars and 51 cents.

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3 years ago

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

If x+1/x= 3 then x-1/x = ?

Alekssandra [29.7K]

Answer:

If x+1/x= 3 Then the answer for this equation (x-1/x=? ) will be...

Step-by-step explanation:

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3 years ago

In the XY coordinate plane, the slope of a line is 4 and it passes through the point (1,3). Find the equation of a line that is

Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

I'm sorry of this answer is wrong

7 0

3 years ago

find two consecutive odd intergers that twice the larger is fifteen more than three times the smaller

Svetach [21]

Answer:

11, 13

Step-by-step explanation:

an odd number can be represented by 2n+1

since they are consecutive, the larger odd number will be 2n + 1 + 2

now,

2(2n+3) = 2n + 1 +15

solving this eqn, we get n = 5

so the two numbers are (2n+1) = 11 and 11+2= 13

4 0

3 years ago

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