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3 years ago

Write the system of equations as an augmented matrix

Mathematics

1 answer:

stepan [7]3 years ago

4 0

Answer: I will answer this but I need a bit more detail :)

Step-by-step explanation:

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A go-kart top speedtop speed is 607,200 ft per hour. what is the speed in miles per hour.

Maru [420]

Divide 607,200 by 5280 which equals 115

6 0

3 years ago

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

Darren's town voted on a new speed limit. 10% of the 20 votes were in favor of the new speed limit. How many votes were in favor

Westkost [7]

10% of 20
20/10 = 2
2 votes were in favour

3 0

3 years ago

What is the measure of T and U

andreev551 [17]

T-> 180-2*(54)= 72° ……

5 0

3 years ago

What is 3 over 4 + b = 3

FromTheMoon [43]

Answer:

2 and 1/4

Step-by-step explanation:

3/4 + b = 3

rearrange the equation

3 - 3/4 = b

3/1 - 3/4 = 14/4 - 3/4 = 11/4 = 2 and 1/4

4 0

3 years ago