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:
3rd option
Step-by-step explanation:
Using the identities
cot x = 
csc² x = 1 + cot² x
Given
tanθ =
, then cotθ = 
csc²θ = 1 + (
)² = 1 +
= 
cscθ = ±
= ± 
Since θ is in 3rd quadrant, then cscθ < 0
cscθ = -
×
= -
Answer:
i think its a <em>knockoff</em>
Step-by-step explanation:
Hello,
The formula for finding the area of a circular region is:

then:

With the two radius it is formed an isosceles triangle, so, we must obtain its area, but first we obtain the height and the base.

Now we can find its area:
![A_{2}=2* \frac{b*h}{2} \\ \\ A_{2}= [r*sen(40)][r*cos(40)]\\ \\A_{2}= r^{2}*sen(40)*cos(40)](https://tex.z-dn.net/?f=A_%7B2%7D%3D2%2A%20%5Cfrac%7Bb%2Ah%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20A_%7B2%7D%3D%20%5Br%2Asen%2840%29%5D%5Br%2Acos%2840%29%5D%5C%5C%20%20%5C%5CA_%7B2%7D%3D%20r%5E%7B2%7D%2Asen%2840%29%2Acos%2840%29)
The subtraction of the two areas is 100cm^2, then:
Answer: r= 1.59cm
It is too blurry to read it get a better camera