Given
![y(3)=1](https://tex.z-dn.net/?f=y%283%29%3D1)
, the solution gives the equation
![1=3^2+\dfrac c{3^2}\implies1=9+\dfrac c9\implies c=-72](https://tex.z-dn.net/?f=1%3D3%5E2%2B%5Cdfrac%20c%7B3%5E2%7D%5Cimplies1%3D9%2B%5Cdfrac%20c9%5Cimplies%20c%3D-72)
so that the particular solution is
![y=x^2-\dfrac{72}{x^2}](https://tex.z-dn.net/?f=y%3Dx%5E2-%5Cdfrac%7B72%7D%7Bx%5E2%7D)
To verify that this solution is correct, differentiate it, then plug it and its derivative into the ODE and arrive at an identity.
![y'=2x+\dfrac{144}{x^3}](https://tex.z-dn.net/?f=y%27%3D2x%2B%5Cdfrac%7B144%7D%7Bx%5E3%7D)
![\implies xy'=2x^2+\dfrac{144}{x^2}](https://tex.z-dn.net/?f=%5Cimplies%20xy%27%3D2x%5E2%2B%5Cdfrac%7B144%7D%7Bx%5E2%7D)
![xy'+2y=4x^2\iff \left(2x^2+\dfrac{144}{x^2}\right)+2\left(x^2-\dfrac{72}{x^2}\right)=4x^2\iff 4x^2=4x^2](https://tex.z-dn.net/?f=xy%27%2B2y%3D4x%5E2%5Ciff%20%5Cleft%282x%5E2%2B%5Cdfrac%7B144%7D%7Bx%5E2%7D%5Cright%29%2B2%5Cleft%28x%5E2-%5Cdfrac%7B72%7D%7Bx%5E2%7D%5Cright%29%3D4x%5E2%5Ciff%204x%5E2%3D4x%5E2)
which is true for all
![x>0](https://tex.z-dn.net/?f=x%3E0)
.
Answer:
because either x-6=0 or x+1=0
x-6=0
x=0+6
x=6 OR,
x+1=0
x=0-1
x=-1
Step-by-step explanation:
We know that
The inscribed angle Theorem states that t<span>he inscribed angle measures half of the arc it comprises.
</span>so
m∠D=(1/2)*[arc EFG]
and
m∠F=(1/2)*[arc GDE]
arc EFG+arc GDE=360°-------> full circle
applying multiplication property of equality
(1/2)*arc EFG+(1/2)*arc GDE=180°
applying substitution property of equality
m∠D=(1/2)*[arc EFG]
m∠F=(1/2)*[arc GDE]
(1/2)*arc EFG+(1/2)*arc GDE=180°----> m∠D+m∠F=180°
the answer in the attached figure
Answer:
x=-2
y=0
Step-by-step explanation:
y=-8x-16
6x-4(-8x-16)=-12
3x-2(-8x-16)=-6
3 x+16 x+32=-6
19x=-6-32=-38x=-2
y=-8(-2)-16=0