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3 years ago

Which expression below is equivalent to 10? 06+1 + 3 012-3 O 5+3+1 015-2-1

Mathematics

1 answer:

GalinKa [24]3 years ago

6 0

Answer:

6 + 1 + 3

Step-by-step explanation:

6 + 1 = 7
7 + 3 = 10

I hope this helps!

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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).

3 0

2 years ago

It S.P. =Rs810, loss percent=10% find C.p

zlopas [31]

Answer:

x=900

Step-by-step explanation:

100-10=90

90/100=0.9

x*0.9=810

x=810/0.9

<em>x=900:)</em>

hope it helps!!

Have a great day

5 0

3 years ago

HELP PLEASEEEEE will choose brainiest answer

Vikki [24]

Answer:

15x -4 = 11x and 4x+5=9x

9 timees11 = 20x

Step-by-step explanation:

20x for first anwer

thank me later emmitheblackbobcat

7 0

3 years ago

Read 2 more answers

Would anyone be willing to helppp? I’ll be giving brainliest when I get the chance too

anyanavicka [17]

Step-by-step explanation:

1. add the numbers all together

(of the pets)

= 40 pets total

40 pets =100%

1 pet = 2.5%

percents:

Cat= 10, or 25%

Dog = 15, or 37.5 %

fish=8 or 20%

bird= 7 or 17.5%

angles:

dog= 135

cat= 90

fish= 72

bird= 63

5 0

3 years ago

Make the smallest 3 digit number that has factor2,3,4,5

Bogdan [553]

2x3x4x5 = 120

answer
120

6 0

4 years ago