Answer:
Step-by-step explanation:
I think you made a typo. g(x) should equal x - 2 not x - 22
g(x) = x - 2
g(-1) = -1 - 2
g(-1) = - 3
The answer is d. Otherwise there is no answer.
If
and
, separate variables in the differential equation to get
![e^{-y} \, dy = \sin(x) \, dx](https://tex.z-dn.net/?f=e%5E%7B-y%7D%20%5C%2C%20dy%20%3D%20%5Csin%28x%29%20%5C%2C%20dx)
Integrate both sides:
![\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20e%5E%7B-y%7D%20%5C%2C%20dy%20%3D%20%5Cint%20%5Csin%28x%29%20%5C%2C%20dx%20%5Cimplies%20-e%5E%7B-y%7D%20%3D%20-%5Ccos%28x%29%20%2B%20C)
Use the initial condition to solve for
:
![-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2](https://tex.z-dn.net/?f=-e%5E%7B-0%7D%20%3D%20-%5Ccos%28-%5Cpi%29%20%2B%20C%20%5Cimplies%20-1%20%3D%201%20%2B%20C%20%5Cimplies%20C%20%3D%20-2)
Then the particular solution to the initial value problem is
![-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2](https://tex.z-dn.net/?f=-e%5E%7B-y%7D%20%3D%20-%5Ccos%28x%29%20-%202%20%5Cimplies%20e%5E%7B-y%7D%20%3D%20%5Ccos%28x%29%20%2B%202)
(A)
Answer:
29.92 m² (nearest hundredth)
Step-by-step explanation:
![\textsf{Area of a sector}=\dfrac{\theta}{360\textdegree}\pi r^2](https://tex.z-dn.net/?f=%5Ctextsf%7BArea%20of%20a%20sector%7D%3D%5Cdfrac%7B%5Ctheta%7D%7B360%5Ctextdegree%7D%5Cpi%20r%5E2)
Area of rectangle = width × length
⇒ area = 4 × 5.5 = 22 m²
Total area = area of sector + area of rectangle
⇒ total area =
= 29.91943148... = 29.92 m² (nearest hundredth)