Answer: To check a solution, you can substitute the solutions into the equations and verify that both equations are true.
Step-by-step explanation:
Answer: The correct point is (1, 0)
In polar coordinates, the first number is the distance from the origin in any direction. The second number is an angle measurement that tells us the direction to go from the origin.
Therefore, we have to move -1 one unit (or backwards) from the origin. Now, all we need to know is the direction to move.
The second number is 180, so we make an angle of 180 degrees and move in that direction.
But where do we start?
We always start from the origin straight right along the x-axis. That is degrees 0. So a 180 degree angle would move us left along the x-axis. But remember, we are moving back 1 space, so we will end up at (1, 0).
Answer:
Yes
Step-by-step explanation:
Is (5,0) , (4,2), (3,4), (2,6), (1,8) a linear function?
Yes, it is a linear function.
Whats the question?......................
Answer:
The probability of the system being down in the next hour of operation is 0.3.
Step-by-step explanation:
We have a transition matrix from one period to the next (one hour) that can be written as:
![T=\left[\begin{array}{ccc}&R&D\\R&0.7&0.3\\D&0.2&0.8\end{array}\right]](https://tex.z-dn.net/?f=T%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26R%26D%5C%5CR%260.7%260.3%5C%5CD%260.2%260.8%5Cend%7Barray%7D%5Cright%5D)
We can represent the state that system is initially running with the vector:
![S_0=\left[\begin{array}{cc}1&0\end{array}\right]](https://tex.z-dn.net/?f=S_0%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5Cend%7Barray%7D%5Cright%5D)
The probabilties of the states in the next period can be calculated using the matrix product of the actual state and the transition matrix:
That is:
![S_1=S_0\cdot T= \left[\begin{array}{cc}1&0\end{array}\right]\cdot \left[\begin{array}{cc}0.7&0.3\\0.2&0.8\end{array}\right]= \left[\begin{array}{cc}0.7&0.3\end{array}\right]](https://tex.z-dn.net/?f=S_1%3DS_0%5Ccdot%20T%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5Cend%7Barray%7D%5Cright%5D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.7%260.3%5C%5C0.2%260.8%5Cend%7Barray%7D%5Cright%5D%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.7%260.3%5Cend%7Barray%7D%5Cright%5D)
With the inital state as running, we have a probabilty of 0.7 that the system will be running in the next hour and a probability of 0.3 that it will be down.
