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2 years ago

How many terms are in the following expression: 8x + 4y + 7 + 22y

Mathematics

2 answers:

Agata [3.3K]2 years ago

4 0

Answer: 3

Step-by-step explanation: Combine Like Terms:

=8x+4y+7+22y

=(8x)+(4y+22y)+(7)

=8x+26y+7

gladu [14]2 years ago

3 0

Answer:

7 is the term

Step-by-step explanation:

the 7 is the term

because 22y is a coeifcent and a var and the rest of the equation is a coeifcent and a var. Besides 7 so 7 is the term

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Subtract 5x−2 from −3x+4 . 2x + 2 −8x+6 8x−6 −8x+2

Vaselesa [24]

Answer: -8x +6

Step-by-step explanation:

- 3x +4 - (5x -2)

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2 years ago

Find the general solution of the given system. dx dt = −6x + 4y dy dt = − 7 4 x + 2y

Alexus [3.1K]

I assume the coefficient on $x$ in the second equation is $-\dfrac74$ . The coefficient matrix

$\begin{bmatrix}-6&4\\\\-\frac74&2\end{bmatrix}$

has eigenvalues given by

$\begin{vmatrix}-6-\lambda&4\\\\-\frac74&2-\lambda\end{vmatrix}=\lambda^2+4\lambda-5=(\lambda+5)(\lambda-1)=0$

The eigenvalues are thus $\lambda_1=-5$ and $\lambda_2=1$ .

For the eigenvalue $\lambda_1$ , the corresponding eigenvector $\eta_1$ satisfies

$\begin{bmatrix}-1&4\\\\-\frac74&7\end{bmatrix}\begin{bmatrix}\eta_{1,1}\\\eta_{1,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}$
$\implies\eta_{1,1}=4\eta_{1,2}$

so that we can choose $\eta_1=\begin{bmatrix}4\\1\end{bmatrix}$ .

For $\lamda_2=1$ , we have

$\begin{bmatrix}-7&4\\\\-\frac74&1\end{bmatrix}\begin{bmatrix}\eta_{2,1}\\\eta_{2,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}$
$\implies7\eta_{2,1}=4\eta_{2,2}$

and we can choose $\eta_2=\begin{bmatrix}4\\7\end{bmatrix}$ for the corresponding eigenvector.

Then the general solution to the ODE system is given by

$\begin{bmatrix}x(t)\\y(t)\end{bmatrix}=C_1\begin{bmatrix}4\\1\end{bmatrix}e^{-5t}+\C_2\begin{bmatrix}4\\7\end{bmatrix}e^t$