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3 years ago

11 with Exponent P 4

Mathematics

1 answer:

Natasha2012 [34]3 years ago

5 0

14,641 dndhshd jehfbd dhdhdh dhdhdh s

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Jules reads that i pint is equivalent to 0.473 he asks his teacher how many liters are in one pint .His teacher responds that th

sleet_krkn [62]

Answer:

Yes

Step-by-step explanation:

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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

Sketch a graph that shows the relationship between

STALIN [3.7K]

Answer: 98g

Step-by-step explanation:Given relationshipSalt >> Honey >> Flour10 >> 14 >> 425 >> 35 >> 10It is easy to determine that the relationship is:14/10 = 35/25 = 1.4y = 1.4x, where y- honey and x- saltIf x = 70, then y is:y = 1.4*70 = 98 g

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3 years ago

A movie theater sold 2,604 tickets in 6 days. they sold the same number of tickets each day. How many tickets did the theater se

puteri [66]

Answer: The movie theater sold 434 a day

Step-by-step explanation:

How I got 434 a day

If you multiply 434 x 6 = 2,604

so they sold 2,604 in 6 days.

Let me know if I did something wrong.

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3 years ago

Six sprinters have qualified for the finals in the 100-meter dash at the ncaa national track meet. in how many ways can the spri

kakasveta [241]

6P3...6 x 5 x 4 = 120.

120 is your answer

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4 years ago

Read 2 more answers

11 with Exponent P 4￼

11 with Exponent P 4