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Oksanka [162]
3 years ago
12

How do I do this? please detail steps.

Mathematics
1 answer:
vladimir2022 [97]3 years ago
7 0
Define
{x} =   \left[\begin{array}{ccc}x_{1}\\x_{2}\end{array}\right]

Then
x₁ = cos(t) x₁(0) + sin(t) x₂(0)
x₂ = -sin(t) x₁(0) + cos(t) x₂(0)

Differentiate to obtain
x₁' = -sin(t) x₁(0) + cos(t) x₂(0)
x₂' = -cos(t) x₁(0) - sin(t) x₂(0)

That is,
\dot{x} =   \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right] x(0)

Note that
\left[\begin{array}{ccc}0&1\\-1&09\end{array}\right]   \left[\begin{array}{ccc}cos(t)&sin(t)\\-sin(t)&cos(t)\end{array}\right] =  \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right]

Therefore
x(t) =   \left[\begin{array}{ccc}0&1\\-1&0\end{array}\right] x(t)

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Convert -√3-i to polar form.
Jlenok [28]

Answer:

-sqrt(3) -i = 2 cis (7pi/6)

Step-by-step explanation:

-sqrt(3) -i

We can find the radius

r = sqrt( (-sqrt(3)) ^2 + (-1) ^2)

  = sqrt( 3 + 1)

  = sqrt(4)

  = 2

theta = arctan (y/x)

          arctan (-1/-sqrt(3))

         arctan (1/sqrt(3))

theta = pi/6

But this is in the first quadrant, and we need it in the third quadrant

Add pi to move it to the third quadrant

theta = pi/6 + 6pi/6

         =7pi/6


-sqrt(3) -i = 2 cis (7pi/6)

6 0
3 years ago
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Brrunno [24]
It would be 1531600

How I did it
 First I divided the percentage by 100. Example >> 0.6/100= 0.006
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In the word "MISSISSIPPI", what is the ratio of the letter p's to letter I's
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Answer:

2:4 or 1/2.Step-by-step explanation:

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Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2.<br><br> f (–2) =
lorasvet [3.4K]

Answer:

f(- 2) =  8

Step-by-step explanation:

To evaluate f(- 2) substitute x = - 2 into f(x) , that is

f(- 2) = 2(-2)^{4} - 4(- 2)³ - 11(- 2)² +3(- 2) - 6

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