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2 years ago

Please help and thank you

Mathematics

2 answers:

bixtya [17]2 years ago

8 0

The answer is 9 for Part A and 18 for Part B

Fantom [35]2 years ago

7 0

Answer:

Step-by-step explanation:

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

6 0

2 years ago

How do u do this ? I'm so confused I really need help

Art [367]

Well what do u need help with can u explain?

5 0

2 years ago

A large bucket of 200 golf balls is divided into 4 smaller buckets. How many golf balls are in each small bucket?

elena-14-01-66 [18.8K]

Answer:

50 golf balls

Step-by-step explanation:

200/4 is 50. I did that because it says the golf balls are DIVIDED into 4 smaller buckets.

To check the answer you do 50 times four.

6 0

2 years ago

Read 2 more answers

Brittany was tracking the increasing temperature in the morning. At 8 a.m., it was 68 degrees Fahrenheit. At 10 a.m., it was 74

AysviL [449]

Im gonna go with A..

4 0

2 years ago

The equation of a line is y= -1/2x - 2. What is the equation of the line that is perpendicular to the first line and passes thro

Fed [463]

If two line are perpendicular. The multiply of their slopes are equal to -1.
First line's slope is: -1/2x because if the line equation is form of y=ax+b a is slope.
Let say second line's slope is m
m.-1/2=-1 so m=2
y=ax+b is general form of linear function/equation. (a=slope)
y=2x+b
If this line passes through the point (2,-2),if we write -2 to y and 2 to x, the equation becomes true.
-2=4+b
b=-6
Thus,
y=2x-6 is true answer.

3 0

3 years ago