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2 years ago

Please help I will give brainliest.

Mathematics

1 answer:

ale4655 [162]2 years ago

8 0

Answer:

a and -b is the answer

Step-by-step explanation:

(x-a)(x+b) = 0

x-a = 0 and x+b = 0

then

x = a and x = -b

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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

2 years ago

The population of a town is 13,000. It decreases at a rate of 5% per year. In about how many years will the population be less t

just olya [345]

This is an exponential decay problem.

Using the equation Y = a *(1-rate)^time

where Y is the future value given as 12,000 and a is the starting value given as 13,000.

The rate is also given as 5%.

The equation becomes:

12,000 = 13,000(1-0.05)^x

12,000 = 13,000(0.95)^x

Divide each side by 13000:

12000/13000 = 0.95^x/13000

12/13 = 0.95^x

Use the natural log function:

x = ln(12/13) / ln(0.95)

x = 1.56 years. ( this will equal 12,000

Round to 2 years it will be less than 12000.

3 0

3 years ago

How do you write the terminating decimal for 3/4

Veronika [31]

Answer:

3/4= 0.75

Step-by-step explanation:

Divide #3 by #4 to get 0.75

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3 years ago

<img src="https://tex.z-dn.net/?f=%5Csf%206x%2B4y-2x" id="TexFormula1" title="\sf 6x+4y-2x" alt="\sf 6x+4y-2x" align="absmiddle"

tangare [24]

Not sure what form you want this in:

Simplified this is 4x+4y

Factorised this is 4(x+y)

3 0

2 years ago

Read 2 more answers

Are the graphs of the lines in the pair parallel? Explain. <br> y = 3/7x+ 11 –3x + 7y = 13

ankoles [38]

Remember that parallel lines have the same slope.

y=3/7x+11 (in slope intercept form already)

-3x+7y=13 (standard form)

Add 3x to both sides, giving you 7y=3x+13, divide by 7 on both sides, giving

y=3/7x+13/7

Since both equations' slopes' are the same, their graphs will be parallel.

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2 years ago