Answer:
D
Step-by-step explanation:
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:
6
Step-by-step explanation:
The range of a data set is the numbers covered by the data. This means that the range is the difference between the minimum and maximum. The minimum is the smallest point, 2, and the maximum is the largest point, 8. Therefore, since 8-2=6, 6 must be the range.
Answer:
142°
Step-by-step explanation:
Answer:
(1, 3) and (4,0)
Step-by-step explanation:
The quadratic function is 
We can rewrite in the form 
The graph is obtained by shifting the parent quadratic function 3 units right and 1 unit down to obtain the parabola shown in the attachment.
The straight line also have equation 
The slope is -1 and y-intercept is 4.
We can easily graph this straight line on the same graph as shown in the attachment.
The two graphs intersected at (4,0) and (1,3).
The solution set is therefore {(x,y)|x=4,y=0 or x=1,y=3}
