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3 years ago

If f(x)=2 (x)^2+5√(x+2) what is the domian

1 answer:

5 0

Note that there is no real square root of a negative number so (x +2) must be greater or equal to 0.

When x + 2 = zero x = -2

So the domain is x>= -2 or in interval notation:

[-2, ∞)

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Find K' if the figure is reflected across the x-axis

snow_lady [41]

<h3>Answer: K ' is at (1, 4)</h3>

Explanation:

Point K is located at (1, -4)

We use the rule that $(x,y) \to (x,-y)$ when reflecting over the x axis.

The x coordinate stays the same, but the y coordinate flips from positive to negative or vice versa.

Therefore, K(1,-4) will move to K ' (1, 4)

5 0

2 years ago

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

2 years ago

Which table represents a direct variation? Table A x 4 6 8 10 y 7 9 11 13 Table B x 4 6 8 10 y 12 18 24 30 Table C x 4 6 8 10 y

Alja [10]

Answer:

Table B

Step-by-step explanation: skidaddle skidoodle you probably know the rest 8)

4 0

2 years ago

Read 2 more answers

Colin has several bottles of water. Each bottle of water holds 3 cups. During the day, he drinks 7 cups of water. How many bottl

Natasha_Volkova [10]

Divide total cups he drank by the # of cups in each bottle.

7 ÷ 3= 2.3333

Since each bottle only holds 3 cups, he drank 3 bottles of water. He didn't drink all the water in the third bottle, but he started drinking the third bottle.

ANSWER: 3 bottles

Hope this helps! :)

4 0

3 years ago

Answer this question if you don't smell like moldy pizza. What is 2 plus 78 divided by 0

olchik [2.2K]

Answer:

infinity

Step-by-step explanation:

3 0

2 years ago