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3 years ago

Simply x-5/7x2+4/x - 6/2x

Mathematics

2 answers:

Marina CMI [18]3 years ago

8 0

Answer:

-32/14x

Step-by-step explanation:

kumpel [21]3 years ago

5 0

I got the answer to be as 7x^2-10x+7 /7x if you were looking to simplify the expression

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Please help please i’ll mark

NeX [460]

Answer:

The answer for your question is "False"

5 0

2 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).

3 0

2 years ago

F(x) = 5x3-2 and g(x) = 2x+1, find (f +g)(x).

Gnom [1K]

Answer:

B. 5x³ + 2x -1

Step-by-step explanation:

(f +g)(x) = f(x) + g(x)

= 5x³ - 2 + 2x + 1

= 5x³ + 2x -1

8 0

3 years ago

(3,4) and (0, 5) write a linear equation

Nina [5.8K]

Answer:

y=-1/3x+5

Step-by-step explanation:

Slope-intercept form

y=mx+b

m => slope

b => y-intercept

Slope

m=(y2-y1)/(x2-x1)=(5-4)/(0-3)=1/(-3)=-1/3

Y-intercept

y=-1/3x+b

5=-1/3(0)+b

5=b

Final equation

y=-1/3x+5

3 0

3 years ago

Find the area of this figure. Sides meet at right angles

Anton [14]

Answer: 51?

Warning!:

I might be wrong because I haven't done this in a long time, so make sure to double-check.

Other than that, I hope this helps!

7 0

3 years ago