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3 years ago

Eight x square minus x square

Mathematics

1 answer:

Ahat [919]3 years ago

4 0

( 8x^2)-(x^2) eight x squared=8x^2 X squared= x^2

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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

PLZZ HELP ME

dimulka [17.4K]

Answer:

125/100 X 105 = 131.25

loan total = $131.25

3 0

3 years ago

Troy received a gift of 100 shares of stock from his grandmother on July 1 of the current year. Troy's grandmother had owned the

kumpel [21]

Troy has a basis of $39 per share

total value of shares is $3900

Step-by-step explanation:

On July 1, the date of the gift, the stock was selling for $39 per share.

Troy's basis in the stock = current value of shares

No need to consider the base rate which is in 15 years ago

The current rate of 100 shares = $39 × 100 = $3900

Troy has a basis of $39 per share

total value of shares is $3900

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4 years ago

Find the rate of change on the table

Aneli [31]

Answer:

Step-by-step explanation:

8 0

3 years ago

Josh wants to pour 70.83 grams of salt into a container. So far, he has poured 39.1 grams. How much more salt should Josh pour?

nadya68 [22]

Answer:

31.73 grams

Step-by-step explanation:

70.83 g - 39.1 g = 31.73 g

6 0

2 years ago