<span>3x''+3x'+7x = 9sin 3t - to begin
then </span>Use the method of undetermined coefficients
![xp=Asin(3t)+Bcos(3t).](https://tex.z-dn.net/?f=xp%3DAsin%283t%29%2BBcos%283t%29.)
Then you need to find <span><span>x′p</span> and <span>x′′p and sub them into equation, that will help you to solve A and B.
</span></span>
![xp=Asin(3t)+Bcos(3t) x'p=3Acos(3t)−3Bsin(3t) x''p=−9Asin(3t)−9Bcos(3t) ](https://tex.z-dn.net/?f=xp%3DAsin%283t%29%2BBcos%283t%29%0A%0Ax%27p%3D3Acos%283t%29%E2%88%923Bsin%283t%29%0A%0Ax%27%27p%3D%E2%88%929Asin%283t%29%E2%88%929Bcos%283t%29%20%0A)
And finally you will have this :
<span><span><span>3<span>x′′</span>+3<span>x′</span>+7x=9sin(3t)</span><span>[−27Asin(3t)−27Bcos(3t)]+[9Acos(3t)−9Bsin(3t)]+[7Asin(3t)+7Bcos(3t)]</span><span>=9sin(3t)</span><span>(−20A+9B)sin(3t)+(−20B+9A)cos(3t)=9sin(3t)</span></span></span>
Answer:
![- 8 - 6i](https://tex.z-dn.net/?f=%20-%208%20-%206i)
Step-by-step explanation:
The given expresion is
![y = {x}^{2} - 2x + 1](https://tex.z-dn.net/?f=y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%202x%20%2B%201)
We want to evaluate this expression when x=3i
We substitute to obtain:
![y = {(3i)}^{2} - 2(3i) + 1](https://tex.z-dn.net/?f=y%20%3D%20%20%7B%283i%29%7D%5E%7B2%7D%20%20-%202%283i%29%20%2B%201)
We simplify to get
![y = {3}^{2} \times {i}^{2} - 6i + 1](https://tex.z-dn.net/?f=y%20%3D%20%20%7B3%7D%5E%7B2%7D%20%20%5Ctimes%20%20%7Bi%7D%5E%7B2%7D%20%20-%206i%20%2B%201)
Recall that
![{i}^{2} = - 1](https://tex.z-dn.net/?f=%20%7Bi%7D%5E%7B2%7D%20%20%3D%20%20-%201)
This implies that:
![y = 9 \times - 1 - 6i + 1](https://tex.z-dn.net/?f=y%20%3D%209%20%5Ctimes%20%20-%201%20-%206i%20%2B%201)
![y = - 9 - 6i + 1](https://tex.z-dn.net/?f=y%20%3D%20%20-%209%20-%206i%20%2B%201)
![y = - 8 - 6i](https://tex.z-dn.net/?f=y%20%3D%20%20-%208%20-%206i)
It's 2 hours will take you a long time to burn calories but it's 2 hours
Answer:
1.65 minutes
Step-by-step explanation:
10 9/10 + 5 3/5 = 16 1/2
16 1/2 divided by 20 = 1.65 or 33/20