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3 years ago

Use the rules for multiplication by powers of 10 to calculate 20 × 100.

Mathematics

2 answers:

motikmotik3 years ago

8 0

$\huge{\text{Hey there!}}$

$\text{Question yourself}\bf{\ How\ many\ times\ does\ 20\ goes\ into\ 100?}$

$\huge{\text{20\ *\ 100 = ?}}$

$\text{If you remember the steps onto how to solve\bf{\ long\ multiplication}}$ $\text{then, you should know how to solve this equation just with more steps!}$

$\huge\boxed{\boxed{\text{Answer: A. 2,000}}}\huge\checkmark$

$\text{Good luck on your assignment and enjoy your day!}$

~ $\huge\frak{LoveYourselfFirst:)}$

charle [14.2K]3 years ago

6 0

20 times 100 is 2000.

2 times 1 is 2 and you add on the three zero's in both numbers to the end of the final number.

so, it would be 2000.

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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).

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4 years ago

Read 2 more answers

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Alexeev081 [22]

Answer:

the answer and explanation of the question is in the picture

Step-by-step explanation:

hope this helps

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