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3 years ago

Select all the situations that can be represented by 1/2⋅5. Explain your choices.

Mathematics

2 answers:

Aneli [31]3 years ago

8 0

....................First 3

And i didnt copy u kishaabbas

Norma-Jean [14]3 years ago

6 0

Answer:

It is the first 3 questions.

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

6 0

3 years ago

Paul and Quinn share some money in a ratio 3:2, Paul gets 60 more than Quinn, how much does Quinn get

wlad13 [49]

Answer: 120

Step-by-step explanation:

3+2=5

Let x be the amount of money to be shared

Paul’s share which is (3/5)x is 60+ Quinn’s share which is (2/5)x

Therefore

(3/5)x= (2/5)x + 60

(3/5)x - (2/5)x= 60

(x/5)=60

Cross multiply

x= 60*5=300

It means that Quinn’s share is (2/5)(300)= 120

7 0

3 years ago

Read 2 more answers

562 ÷ Choose... = 14 R2

Zolol [24]

Answer:

7868

Step-by-step explanation:

⇒ This can be written algebraically (with a variable x) as:

562 ÷ x = 14

⇒ Convert the division as a fraction:

$\frac{562}{x}$ = 14

⇒ Multiply both sides by 562 to get rid of the fraction and to isolate the variable x:

562 · $\frac{562}{x}$ = 14 · 562

⇒ Simplify:

x = 7868

Answer: 7868

Hope this helps! :)

4 0

3 years ago

5 x minus 10 y = 30 what is the first step to find x

chubhunter [2.5K]

Move X to the other side with the 30.

3 0

3 years ago

18 - 2x = y

DerKrebs [107]

B. Y equals 0, because if you plug it in ( multiply 2 by 9 ) you will get 18-18 which equals 0.

6 0

3 years ago