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3 years ago

Exprees the ratio 3 inches to 3 feet(12 inches = 1 foot)

Mathematics

1 answer:

taurus [48]3 years ago

7 0

Ratio being 12in./1ft.

3 inches is not one foot. it's 1/4 of a foot. 3in./1/4ft.

3 feet = 36 inches.

36in./3ft.

Hope This Helped! Good Luck!

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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

Tory is solving the equation shown correctly in her notebook, but the paper gets smudged, and she cannot read the last few lines

elena55 [62]

This question is incomplete because the options are missing. Here are the options:

A. - 4 = 5x

B. -4 = x

C. -4 + x = 0

D. -4 + 5x = 0

The correct next line of the solution is A. -4 = 5x

An equation is:

A mathematical expression that represents mathematical equality between two expressions.

It has two expressions and is separated by the equal sign, called members.

It has known elements and unknown or unknown data represented with letters like x

According to the above, it can be inferred that the correct answer is option A. because it expresses the correct values according to the operations that have been carried out in the previous lines.

Learn more in: brainly.com/question/10413253

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3 years ago

Hello people ~<br>factorise : 5x²+16x+3

son4ous [18]

5x²+16x+3
5x²+15x+x+3
5x(x+3)+1(x+3)
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Done!

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2 years ago

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si cinco son blancas como va a ver una negra ?

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3 years ago

Solve by unfolding: a0=2, and, n>=1, a_n=7a_n-1.

vodomira [7]

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Check: What is the first term? We expect it is 2. 2(7)^(1-1) = 2(1) = 2. Correct.

What is the third term? We expect it is 98. 2(7)^(3-1) = 2(7)^2 = 98. Right.<span />

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3 years ago