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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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-n+(-3)+3n+5<br><br> Combing like terms :
Karolina [17]

Answer: 2n + 2 should be your answer

3 0
2 years ago
Gorge was able to solve 36 math problems in 15 muinutes. Urban was able to solve 42 math problems in 20 muinutes. Who was able t
MrRissso [65]

Answer:

Urban, 2.1 mins

Step-by-step explanation:

36 ÷ 3 = 2 (Gorge's)

42  ÷ 2 = 2.1 (Urban)

3 0
3 years ago
Please help!
Mandarinka [93]

Answer:0.11111111111

Step-by-step explanation:0.1 with a repeating decimal over the 1 because when you multiply 1/3 by 1/3 thats what you get.

8 0
3 years ago
A bag of marbles has 5 green, 2 yellow, 8 red, and 3 purple marbles. What is the probability of picking a red marble, not replac
hram777 [196]
Sample space ={5G, 2Y, 8R, 3P} =18 POSSIBLE OUTCOME

1st draw: P(R) = 8/18 = 4/9 = 0.444
2nd draw (no replacement, means already one Red is picked up, so the sample space has been reduced): P(another one more RED) = 7/17 =0.411 
7 0
3 years ago
Examine the diagram at right. The smaller triangle (inside of the larger triangle) is similar to larger triangle. How can you so
olchik [2.2K]

As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.

In order to solve for x we can set up the proportion between the horizontal and vertical sides:

28\div 11.2 = 27+x \div x

Solving this proportion for x implies x=18

Now you can solve for m and p using the pythagorean theorem, because both triangles are right:

m = \sqrt{18^2+11.2^2} =21.2

Then, we know that the hypothenuse of the big triangle is m+p, so we have

m+p=\sqrt{(18+27)^2+28^2} = 53

which implies

p = 53-p = 53-21.2=31.8

6 0
3 years ago
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