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)
Answer:
A cross section is the intersection of a figure in three-dimensional space with a plane. A cross section is the face you obtain by making a "slice" through a solid object. A cross section is two-dimensional. We see cross sections in everyday life.
Answer:
B
Step-by-step explanation:
Let's say that the smallest is called "a"
We can re-write the question like this:
a+(a+1)+(a+2)+(a+3) = 174
4a+6=174
4a=168
a=42
Answer:
DONT KNOW TO BE HONEST SEVRS ARE SWAMPED
Step-by-step explanation:
Answer:
a) -15 unites per dollar
b) -12 units per dollar
c) -18 units per dollar
Step-by-step explanation:
We are given the following in the question:
where N(p) is the number of boxes of nails at p dollars per box.
a) average rate of change of demand for a change in price from $2 to $3.
Average rate of change =
b) instantaneous rate of change of demand when the price is $2
Instantaneous rate =
The instantaneous rate of change of demand when the price is $2 is decreasing at 12 units per dollar.
c) instantaneous rate of change of demand when the price is $3
Instantaneous rate =
The instantaneous rate of change of demand when the price is $3 is decreasing at 18 units per dollar.
