Answer:
v=2πrh
r=d/2=8/2=4
Therefore, V=2×3.142×4×2= 50.272 ans.
Answer:
C = 6.28 in.
A = 3.14 in.^2
Step-by-step explanation:
C = (pi)d
C = 3.14 * 2 in.
C = 6.28 in.
A = (pi)r^2
r = d/2 = 2 in./2 = 1 in.
A = 3.14 * (1 in.^2)
A = 3.14 in.^2
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)
