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3 years ago

PLS HELP MEE

Mathematics

1 answer:

nekit [7.7K]3 years ago

6 0

They are similar , scale factor is 3

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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

3 years ago

Help will give brainliest

horrorfan [7]

Answer:

Step-by-step explanation:

i don’t have time now but i promise i’ll give it when i have time

7 0

3 years ago

Read 2 more answers

The combined volume of two identical cubes is 250 cubic centimeters. What is the measure of one cubes edge how do you determine

klio [65]

T_T T-T XD XP ---------------------00000__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

8 0

3 years ago

1. Solve for x.<br> 55°<br> (3r + 23)<br> 75°

Mnenie [13.5K]

Answer:

The value of x is 9.

Step-by-step explanation:

55°

(3 x + 23)

75°

The sum of all the angles of triangle is 180°.

55 + 3 x + 23 + 75 = 180

3 x = 27

x = 9

So, the value of x is 9.

5 0

3 years ago

Variable m is 9 more than variable p. Variable m is also 8 less than variable p. Which pair of equations best models the relatio

mrs_skeptik [129]

Answer:

the answer would be 1 but there are no equations

Step-by-step explanation:

4 0

3 years ago