Answer: The last option, Stacy is incorrect because she should multiply 2 and 2 first and then subtract 4 from 12.
Step-by-step explanation:
We must follow the Order of Operations, also known as PEMDAS. See attached. Multiplication comes before subtraction, but Stacy subtracted 2 from 12 when she should have multiplied 2 by 2. This means the answer to your question is;
Stacy is incorrect because she should multiply 2 and 2 first and then subtract 4 from 12.
Answer:
STUDY OR TUTOURStep-by-step explanation:
Define
![{x} = \left[\begin{array}{ccc}x_{1}\\x_{2}\end{array}\right]](https://tex.z-dn.net/?f=%7Bx%7D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B1%7D%5C%5Cx_%7B2%7D%5Cend%7Barray%7D%5Cright%5D%20)
Then
x₁ = cos(t) x₁(0) + sin(t) x₂(0)
x₂ = -sin(t) x₁(0) + cos(t) x₂(0)
Differentiate to obtain
x₁' = -sin(t) x₁(0) + cos(t) x₂(0)
x₂' = -cos(t) x₁(0) - sin(t) x₂(0)
That is,
![\dot{x} = \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right] x(0)](https://tex.z-dn.net/?f=%5Cdot%7Bx%7D%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-sin%28t%29%26cos%28t%29%5C%5C-cos%28t%29%26-sin%28t%29%5Cend%7Barray%7D%5Cright%5D%20x%280%29)
Note that
![\left[\begin{array}{ccc}0&1\\-1&09\end{array}\right] \left[\begin{array}{ccc}cos(t)&sin(t)\\-sin(t)&cos(t)\end{array}\right] = \left[\begin{array}{ccc}-sin(t)&cos(t)\\-cos(t)&-sin(t)\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%5C%5C-1%2609%5Cend%7Barray%7D%5Cright%5D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dcos%28t%29%26sin%28t%29%5C%5C-sin%28t%29%26cos%28t%29%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-sin%28t%29%26cos%28t%29%5C%5C-cos%28t%29%26-sin%28t%29%5Cend%7Barray%7D%5Cright%5D%20)
Therefore
<span>Let x=0.8888...
x=0.8888 Start with the given equation
10x=8.8888 Multiply both sides by 10. The goal is to move the decimal point to the next repeating portion (which is just one spot to the right)
Now subtract the equation x=0.8888 from 10x=8.8888 to get
10x-x=8.8888-0.8888
9x=8 Combine like terms. Notice how the decimal portions cancel out.
x=8/9 Divide both sides by 9 to isolate x
So the answer is x=8/9 which means that 8/9=0.8888 (where the 8's repeat)</span>
Number 4 is 66
Number 5 Iseconds 5.32