Answer:
To calculate the volume of a cylinder, you need the radius or diameter of the circular base or top and the height of the cylinder. The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.
B is right I think because it changes the point from b to a instead of a to b
Y=5. Just substitute 1 in for x because a coordinate in (x,y) and then when you do that you get ...
y=3(1) +2
y=3+2
y=5
(1,5)
Answer:
Step-by-step explanation:
We are given the following differential equation:
![y dx = 2(x + y) dy](https://tex.z-dn.net/?f=y%20dx%20%3D%202%28x%20%2B%20y%29%20dy)
We have to substitute
![x = vy](https://tex.z-dn.net/?f=x%20%3D%20vy)
Differentiating we get,
![\dfrac{dx}{dy} = v + y\dfrac{dv}{dy}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%7D%7Bdy%7D%20%3D%20v%20%2B%20y%5Cdfrac%7Bdv%7D%7Bdy%7D)
Putting value in differential equation, we get,
![y dx = 2(x + y) dy\\\\y\dfrac{dx}{dy}=2(x+y)\\\\y(v+y\dfrac{dv}{dy}) = 2(vy + y)\\\\vy + y^2\dfrac{dv}{dy} = 2vy +2y\\\\y^2\dfrac{dv}{dy}=vy +2y\\\\y^2dv = y(v+2)dy\\ydv = (v +2)dy\\](https://tex.z-dn.net/?f=y%20dx%20%3D%202%28x%20%2B%20y%29%20dy%5C%5C%5C%5Cy%5Cdfrac%7Bdx%7D%7Bdy%7D%3D2%28x%2By%29%5C%5C%5C%5Cy%28v%2By%5Cdfrac%7Bdv%7D%7Bdy%7D%29%20%3D%202%28vy%20%2B%20y%29%5C%5C%5C%5Cvy%20%2B%20y%5E2%5Cdfrac%7Bdv%7D%7Bdy%7D%20%3D%202vy%20%2B2y%5C%5C%5C%5Cy%5E2%5Cdfrac%7Bdv%7D%7Bdy%7D%3Dvy%20%2B2y%5C%5C%5C%5Cy%5E2dv%20%3D%20y%28v%2B2%29dy%5C%5Cydv%20%3D%20%28v%20%2B2%29dy%5C%5C)
is the differential equation after substitution.