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:
1.) 112.5 degrees
2.) 67.5 degrees
3.) 150 degrees
4.) 240 degrees
5.) 540 degrees
( don't hate me if any is wrong don't think they are but just trying to help) let me know if any of them are wrong and if it helped!
The domain of G is 4 and the range of G is 9 (domain=x, range=y :))
The graphs of the functions y = 4(2ˣ + 3) - 1 and y = - 2(3ˣ - 4) + 1 are plotted on the graph.
<h3>What is function?</h3>
A function is a relation between a dependent and a independent variable, such that the dependent variable depends upon the independent one for its existence.
Given are the following functions -
y = 4(2ˣ + 3) - 1
y = - 2(3ˣ - 4) + 1
We have the following functions -
y = 4(2ˣ + 3) - 1
y = - 2(3ˣ - 4) + 1
Refer to the graph attached. The graph of red color represents the function y = 4(2ˣ + 3) - 1 and the graph of blue color represents the function y = - 2(3ˣ - 4) + 1. It can be seen that the graphs are symmetrical about the line y = 10.
Therefore, the graphs of the functions y = 4(2ˣ + 3) - 1 and y = - 2(3ˣ - 4) + 1 are plotted on the graph.
To solve more questions on plotting graphs, visit the link below-
brainly.com/question/14299685
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Answer:
5
Step-by-step explanation:
3 bears = 3
1 bear = 3 ÷ 3
1 bear = 1
2 glasses + 1 bear = 5
2 glasses + 1 = 5
2 glasses = 5 - 1
= 4
1 glasses = 4 ÷ 2
1 glasses = 2
1 Cyxus + 1 bear + 1 Cyxus + 1 glasses = 9
2 Cyxus + 1 + 2 = 9
2 Cyxus = 9 - 1 - 2
= 6
1 Cyxus = 6 ÷ 2
1 Cyxus = 3
1 glasses + 1 bear + 1 glasses + 1 Cyxus - 1 bear - 1 glasses = ?
2 + 1 + 2 + 3 - 1 - 2 = 5