Answer:
if triangles are congruent if three pairs of corresponding sides are
congruent.to made a congruent triangle
following axiom need to fulfilled.
- A.S.A AXIOM
- S.S.S. AXIOM
- S.A.S. AXIOM
The answer is b
There is no solution to the problem because it just doesn’t make sense. You can not add to sides with so many variables and expect to get a answer
Answer:
x-axis = ![\frac{9\pi }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B9%5Cpi%20%7D%7B2%7D)
y-axis = ![\frac{4\pi }{5} .3(^{\frac{5}{2} } )](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20%7D%7B5%7D%20.3%28%5E%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29)
Line x =3 : ![\frac{44\sqrt{3} }{5} \pi](https://tex.z-dn.net/?f=%5Cfrac%7B44%5Csqrt%7B3%7D%20%7D%7B5%7D%20%5Cpi)
Line x = 6 : ![\frac{84\sqrt{3}\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B84%5Csqrt%7B3%7D%5Cpi%20%20%7D%7B5%7D)
Step-by-step explanation:
Given lines : y = √x
y = 0
x = 3
To determine the volumes generated we will use the disk method for each of the lines,
attached below is the detailed solution for line x =3 , same procedure will be repeated for each value of x and y to obtain the given results
The volume generated ( x axis )
= ![\frac{9\pi }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B9%5Cpi%20%7D%7B2%7D)
volume generated ( y _axis )
= ![\frac{4\pi }{5} .3(^{\frac{5}{2} } )](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20%7D%7B5%7D%20.3%28%5E%7B%5Cfrac%7B5%7D%7B2%7D%20%7D%20%29)
Volume about x = 3
= ![\frac{44\sqrt{3}\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B44%5Csqrt%7B3%7D%5Cpi%20%20%7D%7B5%7D)
Volume about x = 6
= ![\frac{84\sqrt{3}\pi }{5}](https://tex.z-dn.net/?f=%5Cfrac%7B84%5Csqrt%7B3%7D%5Cpi%20%20%7D%7B5%7D)
Answer:
Step-by-step explanation: I did the test and the answer should be A
hope this helps :)
Answer:
a.![y(x)=C_1x^{-1}+C_2x^{-8}+\frac{1}{30}x^2](https://tex.z-dn.net/?f=y%28x%29%3DC_1x%5E%7B-1%7D%2BC_2x%5E%7B-8%7D%2B%5Cfrac%7B1%7D%7B30%7Dx%5E2)
b.![y(x)=x^2(C_1cos (3lnx)+C_2sin(3lnx))+\frac{4}{13}+\frac{3}{10}x](https://tex.z-dn.net/?f=y%28x%29%3Dx%5E2%28C_1cos%20%283lnx%29%2BC_2sin%283lnx%29%29%2B%5Cfrac%7B4%7D%7B13%7D%2B%5Cfrac%7B3%7D%7B10%7Dx)
Step-by-step explanation:
1.![x^2y''+10xy'+8y =x^2](https://tex.z-dn.net/?f=x%5E2y%27%27%2B10xy%27%2B8y%20%3Dx%5E2)
It is Cauchy-Euler equation where ![x=e^t](https://tex.z-dn.net/?f=x%3De%5Et)
Then auxillary equation
![D'(D'-1)+10D'+8=0](https://tex.z-dn.net/?f=D%27%28D%27-1%29%2B10D%27%2B8%3D0)
![D'^2+9D'+8=0](https://tex.z-dn.net/?f=D%27%5E2%2B9D%27%2B8%3D0)
![(D'+1)(D'+8)=0](https://tex.z-dn.net/?f=%28D%27%2B1%29%28D%27%2B8%29%3D0)
D'=-1 and D'=-8
Hence, C.F=![C_1e^{-t}+C_2e^{-8t}](https://tex.z-dn.net/?f=C_1e%5E%7B-t%7D%2BC_2e%5E%7B-8t%7D)
C.F=![C_1\frac{1}{x}+C_2\frac{1}{x^8}](https://tex.z-dn.net/?f=C_1%5Cfrac%7B1%7D%7Bx%7D%2BC_2%5Cfrac%7B1%7D%7Bx%5E8%7D)
P.I=![\frac{e^{2t}}{D'^2+9D'+8}=\frac{e^{2t}}{4+18+8}](https://tex.z-dn.net/?f=%5Cfrac%7Be%5E%7B2t%7D%7D%7BD%27%5E2%2B9D%27%2B8%7D%3D%5Cfrac%7Be%5E%7B2t%7D%7D%7B4%2B18%2B8%7D)
Where D'=2
![P.I=\frac{1}{30}e^{2t}=\frac{1}{30}x^2](https://tex.z-dn.net/?f=P.I%3D%5Cfrac%7B1%7D%7B30%7De%5E%7B2t%7D%3D%5Cfrac%7B1%7D%7B30%7Dx%5E2)
![y(x)=C_1x^{-1}+C_2x^{-8}+\frac{1}{30}x^2](https://tex.z-dn.net/?f=y%28x%29%3DC_1x%5E%7B-1%7D%2BC_2x%5E%7B-8%7D%2B%5Cfrac%7B1%7D%7B30%7Dx%5E2)
b.![x^2y''-3xy'+13y=4+3x](https://tex.z-dn.net/?f=x%5E2y%27%27-3xy%27%2B13y%3D4%2B3x)
Same method apply
Auxillary equation
![D'^2-D'-3D'+13=0](https://tex.z-dn.net/?f=%20D%27%5E2-D%27-3D%27%2B13%3D0)
![D'^2-4D'+13=0](https://tex.z-dn.net/?f=D%27%5E2-4D%27%2B13%3D0)
![D'=2\pm3i](https://tex.z-dn.net/?f=D%27%3D2%5Cpm3i)
C.F=![e^{2t}(C_1cos 3t+C_2sin 3t)](https://tex.z-dn.net/?f=e%5E%7B2t%7D%28C_1cos%203t%2BC_2sin%203t%29)
C.F=![x^2(C_1cos (3lnx)+C_2sin(3lnx))](https://tex.z-dn.net/?f=x%5E2%28C_1cos%20%283lnx%29%2BC_2sin%283lnx%29%29)
![e^t=x](https://tex.z-dn.net/?f=e%5Et%3Dx)
P.I=![\frac{4e^{0t}}{D'^2-4D'+13}+3\frac{e^t}{D'^2-4D'+13}](https://tex.z-dn.net/?f=%5Cfrac%7B4e%5E%7B0t%7D%7D%7BD%27%5E2-4D%27%2B13%7D%2B3%5Cfrac%7Be%5Et%7D%7BD%27%5E2-4D%27%2B13%7D)
Substitute D'=0 where
and D'=1 where ![e^t](https://tex.z-dn.net/?f=e%5Et)
P.I=![\frac{4}{13}+\frac{3}{10}e^t](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B13%7D%2B%5Cfrac%7B3%7D%7B10%7De%5Et)
P.I=![\frac{4}{13}+\frac{3}{10}x](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B13%7D%2B%5Cfrac%7B3%7D%7B10%7Dx)
![y(x)=C.F+P.I=x^2(C_1cos (3lnx)+C_2sin(3lnx))+\frac{4}{13}+\frac{3}{10}x](https://tex.z-dn.net/?f=y%28x%29%3DC.F%2BP.I%3Dx%5E2%28C_1cos%20%283lnx%29%2BC_2sin%283lnx%29%29%2B%5Cfrac%7B4%7D%7B13%7D%2B%5Cfrac%7B3%7D%7B10%7Dx)