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3 years ago

Will someone please help asappp

Mathematics

2 answers:

Zigmanuir [339]3 years ago

8 0

Answer:

your answer would be postitive 10

Tcecarenko [31]3 years ago

5 0

Answer:

idw lolklo

Step-by-step explanation:

I got you trust me bro love you

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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

Computer models are systems of mathematical equations that describe the behavior of the atmosphere. Select one: True False

Assoli18 [71]

Answnser: True

Step-by-step explanation:

4 0

2 years ago

Free points: this is because of all the kindness I have seen on brainly:

const2013 [10]

Answer:

10x10= 100

Step-by-step explanation:

thx for the points

hope you have a wonderful dayyy

3 0

3 years ago

Read 2 more answers

Find the center of the circle that can be circumscribed about EFG with E(4, 4), F(4, 2), G(8, 2). (3, 6) (4, 2) (4, 4) (6, 3)

Lesechka [4]

Answer:

(6,3)

Step-by-step explanation:

8 0

3 years ago

3) g(x)= x3 + x<br> h(x) = x + 4<br> Find g(0)h(0)

Arte-miy333 [17]

Answer:

$goh(x)=x^3+12x^2+49x+68$

Step-by-step explanation:

$g(x) = x^3+x$

$h(x)=x+4$

We have to find

$goh(x)$

$goh(x) = g(h(x))=g(x+4)$

If $g(x) = x^3+x$

$g(x+4) = (x+4)^3+(x+4)$

= $x^3+12x^2+49x+68$

Hence our answer is

$goh(x)=x^3+12x^2+49x+68$

4 0

3 years ago