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3 years ago

Need help, it’s an assignment ‍♀️

Mathematics

1 answer:

iris [78.8K]3 years ago

7 0

1. copying

3. arc

4. ridgid motion

5. Distance Formula

6. image

7. transformation

8. translation

I don't really know if these are correct because I have never had to define any of those words or know a lot of these. But some of them I am pretty sure are right. I hope I helped some. I am sorry if I didn't. But this is my best guess.

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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: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

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3 years ago

Nico did 42 push-ups in 3 minutes.

Luda [366]

Answer:

14 pushups per min

70 pushups in 5 min

Step-by-step explanation:

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What is the unit rate for meters per second if a car travels 238 meters in 17 seconds?

madreJ [45]

I assume a unit rate is simply ms^-1 or whatever.

In order to determine m/s one must make the "per whatever" part equal to 1. In this case it is seconds, so we must make seconds equal to 1.

If in 17 seconds it travels 238 metres, that means in 1 second it travels 238/17m=14m

Therefore the unit rate (speed) of the car is 14m/s or 14ms^-1

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dlinn [17]

Answer:

the correct anwser is B................

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