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3 years ago

What is the value of the expression 4rs if r = -1/3 and s = 7/8

Mathematics

1 answer:

Brut [27]3 years ago

6 0

1 and 1/6 is the correct answer because 4/1 multiplied by 1/3 is 4/3. 4/3 multiplied by 7/8 is 28/24 or 1 and 4/24, which can be simplified down to 1 and 1/6.

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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

Evaluate the expression m÷n for m=2 and n=14.

Sever21 [200]

Answer:

1/7

Step-by-step explanation:

Plug in 2 for m, and 14 for n in the expression:

m/n = 2/14

Simplify. Factor out common factors from both the numerator and denominator:

(2/14)/(2/2) = 1/7

1/7 is your answer.

3 0

3 years ago

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70<br> 239<br> Answer: 2<br> Submit Answer<br> IN MAJOR NEED OF HELP QUICK

AnnZ [28]

Answer:

X = 67°

Step-by-step explanation:

The sum of every triangle’s interior angles is 180°. First subtract the given angle, 23°, from 180°. This equals 157°. Next you can see that one of the triangle’s angles has a right angle mark. This mark means it’s a right angle and all right angles are 90°. Take 157° and subtract 90°. This equals 67°. This means the remaining angle equals 67°.

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3 years ago

Please help, personal finance question

yawa3891 [41]

I think he would expect $60,000

I hope thats right,
QueenBeauty666

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3 years ago

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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each

balu736 [363]

Answer:

35-=13 boxes ; 65-9 boxes

Step-by-step explanation:

35 x X+ 65 (22-x)=1040

35x+1430-65x=1040

1430-30x=1040

30x=390

x =390/30=13

6 0

3 years ago