# Thread: math homework that i just can't solve.

1. ## math homework that i just can't solve.

Yes so i have some math assighments i need to solve and i am almost done (yes it is for a grade) but i just have problems with it. I need answers for these 2 problems:

1. Cody, Ray, and Amanda are kicking a soccerball. Cody always kicks to Ray, and Ray always kicks to Amanda, but Amanda is equally likely to kick the ball to either Cody or Ray. Find the stable-state vector and tell what it means.

2. The B & M Company produces batteries and motors. The battery division requires 3 batteries from the battery division and 1 motor from the motor division to produce 100 batteries. The motor division requires 4 motors from the motor division and 8 batteries from the battery division to produce 100 motors. B & M has received an order for 900 batteries and 400 motors. Determine the total production needed from each division to fill the order.

2. Hello, lsk91!

1. Cody, Ray, and Amanda are kicking a soccerball.
Cody always kicks to Ray, and Ray always kicks to Amanda,
but Amanda is equally likely to kick the ball to either Cody or Ray.

Find the stable-state vector and tell what it means.
The Markov process is designated by: . $A \;=\;\left(\begin{array}{ccc}0&1&0 \\ 0&0&1 \\ \frac{1}{2} & \frac{1}{2} & 0 \end{array}\right)$

The steady-state vector is: . $\vec v \:=\:( p,q,r)$

. . where: . $(p,q,r )\cdot A \:=\: (p,q,r) \:\text{ and }\:p+q+r\:=\:1$

We have: . $(p,q,r)\cdot\left(\begin{array}{ccc}0&1&0 \\ 0&0&1 \\ \frac{1}{2}&\frac{1}{2}&0 \end{array}\right) \;=\;(p.q.r)$

. . . . . . . $\begin{Bmatrix}\frac{1}{2}r &=& p \\ p+\frac{1}{2}r &=& q \\ q &=& r \end{Bmatrix}\;\;\text{ and: }\;p+q+r\:=\:1$

Solve the system: . $\boxed{(p,q,r) \;=\;\left(\frac{1}{5},\:\frac{2}{5},\:\frac{2}{5} \right)}$

After a very large number of consecutive kicks,
. . there are the probabilities of who has the ball.

. . $\begin{array}{ccc}P(\text{Cody has the ball}) &=& \dfrac{1}{5} \\ \\[-3mm]
P(\text{Ray has the ball}) &=& \dfrac{2}{5} \\ \\[-3mm]
P(\text{Amanda has the ball}) &=& \dfrac{2}{5} \end{array}$

3. thank you