Answer:
y = x*sqrt(Cx - 1)
Step-by-step explanation:
Given:
dy / dx = (x^2 + 5y^2) / 2xy
Find:
Solve the given ODE by using appropriate substitution.
Solution:
- Rewrite the given ODE:
dy/dx = 0.5(x/y) + 2.5(y/x)
- use substitution y = x*v(x)
dy/dx = v + x*dv/dx
- Combine the two equations:
v + x*dv/dx = 0.5*(1/v) + 2.5*v
x*dv/dx = 0.5*(1/v) + 1.5*v
x*dv/dx = (v^2 + 1) / 2v
-Separate variables:
(2v.dv / (v^2 + 1) = dx / x
- Integrate both sides:
Ln (v^2 + 1) = Ln(x) + C
v^2 + 1 = Cx
v = sqrt(Cx - 1)
- Back substitution:
(y/x) = sqrt(Cx - 1)
y = x*sqrt(Cx - 1)
We are given coordinates of the triangle: A(2,2), B(7,1) and C(8,-4).
We need to rotated 90° counterclockwise about the origin.
In order to find the new coordinates of rotatation 90°counterclockwise about the origin, we can apply rule (h, k) ---> (-k,h).
Where (h,k) are the coordinates of original image on axes and (-k,h) are the coordinates of rotated image.
In resulting coordinates of the image first swap the x and y coordinates of the original image and then make the sign opposite of each x-coordinate.
On applying rule (h, k) ---> (-k,h), we get
A(2,2) --> A'(-2,2)
B(7,1) --> B'(-1,7)
C(8,-4) --> C'(4,8)
Answer:
Step-by-step explanation:
5 is in the hundreds place.
The answer should be 213500
Answer:
3.5
Step-by-step explanation:
Answer:
A is 4
Step-by-step explanation:
A _ 8 _ _ _ _ _ _ _ _ 8 _ 6
A _ 8 _ _ _ _ _ _ _ _ 8 4 6
A _ 8 _ _ _ _ _ _ _ 6 8 4 6
A _ 8 _ _ _ _ _ _ 4 6 8 4 6
A _ 8 _ _ _ _ _ 8 4 6 8 4 6
A _ 8 _ _ _ _ 6 8 4 6 8 4 6
A _ 8 _ _ _ 4 6 8 4 6 8 4 6
A _ 8 _ _ 8 4 6 8 4 6 8 4 6
A _ 8 _ 6 8 4 6 8 4 6 8 4 6
A _ 8 4 6 8 4 6 8 4 6 8 4 6
A 6 8 4 6 8 4 6 8 4 6 8 4 6
4 6 8 4 6 8 4 6 8 4 6 8 4 6
A is 4
Hope this helps!
