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2 years ago

PUPUL 2

Mathematics

1 answer:

grandymaker [24]2 years ago

4 0

Answer:

37.045

Step-by-step explanation:

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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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2 years ago

Antonio had his hair cut at the salon. After he returned home, he realized he had accidentally tipped the stylist 114% of the co

stepan [7]

=>C

1.14*20.95=23.883

5 0

2 years ago

Write all your answers as a fraction.<br> 1. 8/3 - 8/5/

allsm [11]

Answer:

16/15

Step-by-step explanation:

Simplify the following:

8/3 - 8/5

Put 8/3 - 8/5 over the common denominator 15. 8/3 - 8/5 = (5×8)/15 + (3 (-8))/15:

(5×8)/15 + (3 (-8))/15

5×8 = 40:

40/15 + (3 (-8))/15

3 (-8) = -24:

40/15 + (-24)/15

40/15 - 24/15 = (40 - 24)/15:

(40 - 24)/15

| 3 | 10

| 4 | 0

- | 2 | 4

| 1 | 6:

Answer: 16/15

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2 years ago

In the recent year 18.2% of all registered doctors were females. If there were 57,000 females registered doctors that year what

harina [27]

Your equation is

0.194*x = 43400,

where x is the unknown total number of registered doctors, which is under the question.

Solve the equation to get the answer:

x = 43400/0.194 = 223711 registered doctors.

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1 year ago

0.99 0.89 7/8 least to greatest

katovenus [111]

From least to greatest 7/8, 0.89, 0.99

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2 years ago