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2 years ago

How to simplify 6 +8b^2 +3b -6 - 10b^2

Mathematics

1 answer:

kozerog [31]2 years ago

5 0

Answer:

-2b^2+3b

Step-by-step explanation:

You just have to add like terms, which is the single numbers, the numbers with just the variables, and the numbers with variables that are squared.

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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

Cleo added 3a+4b and got 7ab. Three of these statements explain why her answer is wrong. Which one does not

Triss [41]

Answer:

3 and 4 are factors of 12 so they should be multiplied to get a product of 12 ab. (Answer D)

Step-by-step explanation:

You do not multiply in addition unless an exponent is present. You should not multiply or add considering these are not like terms. Therefore, D is wrong.

5 0

3 years ago

Solve for r<br> 2r = 7/10

deff fn [24]

Answer:

7/20

Step-by-step explanation:

given,

2r = 7/10

r= 7/10*1/2

r= 7/20

6 0

2 years ago

I need help I will rate you brainliest

Tems11 [23]

Answer:

it would be subtraction

Step-by-step explanation:

Because if you are trying to get you would do 2-2 to get 0 and have x by itself

3 0

3 years ago

Read 2 more answers

05.06)Kent walked to the bus stop, then sat and waited until the bus arrived. He rode the bus for 25 minutes, then walked the la

grandymaker [24]

Answer:

The first one

Step-by-step explanation:

Mark me brainliest please

6 0

2 years ago