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3 years ago

: Question Help

Mathematics

1 answer:

Mrac [35]3 years ago

6 0

Answer: 12 pounds

Step-by-step explanation:

0.80x + 3 = $12.60

-3 -3

0.80x = $9.60

9.60 / 0.80 = 12

x = 12 pounds

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if each interior angle of a regular convex polygon is three times the measure of each exterior angle, what kind of polygon is it

Julli [10]

The interior angle of a regular polygon is equal to 180(n - 2)/n. The exterior angle is always equal to 360/n. Using the given relationship from the item above, the equation that can be formed is,

180(n - 2)/ n = 3(360/n)

The value of n from the equation is 8. The polygon with 8 sides is an octagon.

<em>Answer: OCTAGON</em>

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4 years ago

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3 years ago

Find the critical points of the surface f(x, y) = x3 - 6xy + y3 and determine their nature.

Vedmedyk [2.9K]

Compute the gradient of $f$ .

$\nabla f(x,y) = \left\langle 3x^2 - 6y, -6x + 3y^2\right\rangle$

Set this equal to the zero vector and solve for the critical points.

$3x^2-6y = 0 \implies x^2 = 2y$

$-6x+3y^2=0 \implies y^2 = 2x \implies y = \pm\sqrt{2x}$

$\implies x^2 = \pm2\sqrt{2x}$

$\implies x^4 = 8x$

$\implies x^4 - 8x = 0$

$\implies x (x-2) (x^2 + 2x + 4) = 0$

$\implies x = 0 \text{ or } x-2 = 0 \text{ or } x^2 + 2x + 4 = 0$

$\implies x = 0 \text{ or } x = 2 \text{ or } (x+1)^2 + 3 = 0$

The last case has no real solution, so we can ignore it.

Now,

$x=0 \implies 0^2 = 2y \implies y=0$

$x=2 \implies 2^2 = 2y \implies y=2$

so we have two critical points (0, 0) and (2, 2).

Compute the Hessian matrix (i.e. Jacobian of the gradient).

$H(x,y) = \begin{bmatrix} 6x & -6 \\ -6 & 6y \end{bmatrix}$

Check the sign of the determinant of the Hessian at each of the critical points.

$\det H(0,0) = \begin{vmatrix} 0 & -6 \\ -6 & 0 \end{vmatrix} = -36 < 0$

which indicates a saddle point at (0, 0);

$\det H(2,2) = \begin{vmatrix} 12 & -6 \\ -6 & 12 \end{vmatrix} = 108 > 0$

We also have $f_{xx}(2,2) = 12 > 0$ , which together indicate a local minimum at (2, 2).

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2 years ago

Please help need answer asp

mariarad [96]

Its really easy. just look at the middle line. now the sides are only the answers including the square roots. so the line in the middle represents 12. The answer is 12

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3 years ago

Kkkkkkkkkkkkkkkkkkkkkkkk

Aloiza [94]

The formula for slope is y = mx + b
y is the y value, m is the slope, x is the x value, and b is the y intercept.

The equation given for line e is
$y = \frac{ - 9}{2} x + 7$
Therefore the slope of line e is -9/2
Line f is parallel and parallel lines have the same slope.

So the slope is line f is -9/2.

The picture isn't that clear and I can't really tell if it's-9/2 or 9/2.
But whatever it is, the slope of line f is the same as the slope of line e because they are parallel.
Good luck!

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4 years ago