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3 years ago

What equation is represented by the equation on the graph ?

Mathematics

1 answer:

solmaris [256]3 years ago

6 0

Answer: The correct option is D.

Explanation:

From the graph we noticed that the x intercept of the line is (2,0) and the y-intercept is (0,2).

If the line passing through two points then the equation of line is,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Since the ien passing through (2,0) and (0,2).

$y-0=\frac{2-0}{0-2}(x-2)$

$y=-1(x-2)$

$y=-x+2$

This equation is represented by option D, therefore the option D is correct.

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2 years ago

Write the given linear system in matrix form. Assume X = x y z . dx dt = −8x + 7y − 9z dy dt = 5x − y dz dt = 10x + 7y + 8z

Akimi4 [234]

Answer:

The matrix form of given linear system is

$\begin{bmatrix}x'\\ y'\\ z'\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

Step-by-step explanation:

Let as assume that

$X=\begin{bmatrix}x\\ y\\ z\end{bmatrix}$

Given differential equations are

$\frac{dx}{dt}=-8x+7y-9z$

$\frac{dy}{dt}=5x-y$

$\frac{dz}{dt}=10x+7y+8z$

We need to find the matrix form of given linear system.

Write the elements of left side in a column matrix.

Write all the coefficients in one matrix first which is called a coefficient matrix. Multiply coefficient matrix with the variables matrix and equate left and right side.

$\begin{bmatrix}\frac{dx}{dt}\\ \frac{dy}{dt}\\ \frac{dz}{dt}\end{bmatrix}=\begin{bmatrix}-8 & 7 &-9\\ 5 & -1 & 0\\ 10 & 7 & 8\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}$