What is the standard form for the equation y=-5x+8

HELP ME THANKS ;) for number 1 through 11 QUICKLY

stiv31 [10]

1>>g
2>>e
3>>h
4>>f
5>>b
6>j
7>>k
8>>c
9>>I
10>>d
11>>a
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4 0

3 years ago

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

Marty is taking piano lessons. She is going to practice every afternoon. The 1st week she practiced for 11 minutes each day. The

defon

Answer:

$m=7w+4$

Step-by-step explanation:

<u>Linear Modeling</u>

It consist is setting up a linear relationship between two variables, given some experimental data. Only 2 points are needed to set up the equation of a line, but if more than 2 points are used, then the result should use statistical approaches like linear regression to find the best-fit line.

For the question at hand, Marty practices his piano lessons 11 minutes the week #1. It provides the first point (1,11). He practices 25 minutes per day on the third week. It gives us another point (3,25). This is enough to find the equation of a line. The general formula for a line, having two points (m1,w1) (m2,w2) is

$\displaystyle m-m_1=\frac{m_2-m_1}{w_2-w_1}(w-w_1)$

Let's plug in our values

$\displaystyle m-11=\frac{25-11}{3-1}(w-1)$

Simplifying:

$m-11=7w-7$

$\boxed{m=7w+4}$

3 0

3 years ago

You check 20 cartons of eggs. Three of the cartons have at least one cracked egg. What is the experimental probability that a ca

Blababa [14]

Answer:

craxk the egg on ur head and see ur answer

Step-by-step explanation:

4 0

3 years ago

Choose the correct option.Immersive Reader (1 Point) (A) z-5=2 is an equation and z=5 is the solution of this equation (B) t+2&g

melomori [17]

Answer:

<h3>Find the explanation below</h3>

Step-by-step explanation:

A) Given the equation z - 5 = 2

To get the solution, we will add 5 to both sides and find z as shown;

z - 5 = 2

z - 5 + 5 = 2 + 5

z + 0 = 2+5

z = 7

Hence z = 5 is not the solution of the equation but z = 7

B) Given the inequality expression t+2>5

Substract 2 from both sides of the equation;

t+2 - 2>5 - 2

t + 0> 3

t>3

Hence the solution t = 4 is not true for the expression. The solution is t > 3

C) Given the expression x-2=2, to get the solution to the expression, you will add 2 to both sides of the equation;

x - 2+ 2 = 2 + 2

x + 0 = 4

x = 4

Therefore x = 4 is the solution of this equation.

Based on the question, only Option C is correct

8 0

3 years ago