The peiod to the left of thousands

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

Valerie had a bottle that was filled with that contained 128oz juice to put into cups, she filled each cup with 6 floz of juice,

Arisa [49]

128/6 to the nearest whole number = 21

21(6) = 126

128 - 126 = 2oz

5 0

2 years ago

Solve this system of equations: y = x2 – 3x + 12 y = –2x + 14 1.Isolate one variable in the system of equations, if needed. y =

lina2011 [118]

-2x+14=x²-3x+12
add 2x on both side:
14=x²-x+12
subtract 14 on both side:
x²-x-2=0
factor: (x-2)(x+1)=0
x=2 or x=-1
HOPE THIS HELPS AND PLEASE MARK ME AS BRAINIEST AND ADD ME AS A FRIEND

8 0

3 years ago

Read 2 more answers

A 6-pound container of detergent costs $4.38. what is the price per pound?

lesya692 [45]

Answer:

.73 per pound

Step-by-step explanation:

Take the total cost and divide by the number of pounds

4.38/ 6

.73 per pound

7 0

2 years ago

Write the percent shown by each model. Explain your reasoning.

Sphinxa [80]

A) 1/3=33 1/3%
B) 2/3=66 2/3%
C) 1/6=16 2/3%

A) YOU CAN TURN THE FRACTION 1/3 INTO A DECIMAL WHICH WILL BE AROUND 0.333. THEN YOU TURN THE DECIMAL INTO A PERCENT. YOU CAN MOVE THE DECIMAL TWO PLACES TO THE RIGHT. THAT GIVES YOU 33.3% OR 33 1/3% THIS ALSO APPLIES TO B BUT WITH 0.666 AND 66.6%

FOR C, YOU DO THE SAME. 1/6 AS A DECIMAL IS 1.666. YOU MOVE THE DECIMAL TWO PLACES TO THE RIGHT. 16.6% OR 16 2/3%

HOPE THIS HELPED.

8 0

2 years ago