Answer:
ok dont get addicted
Step-by-step explanation:
The ODE has characteristic equation
![r^2+6r+9=(r+3)^2=0](https://tex.z-dn.net/?f=r%5E2%2B6r%2B9%3D%28r%2B3%29%5E2%3D0)
with roots
, and hence the characteristic solution
![y_c=C_1e^{-3t}+C_2te^{-3t}](https://tex.z-dn.net/?f=y_c%3DC_1e%5E%7B-3t%7D%2BC_2te%5E%7B-3t%7D)
For the particular solution, assume an ansatz of
, with derivatives
![\dfrac{\mathrm dy_p}{\mathrm dt}=-ae^{-t}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20dy_p%7D%7B%5Cmathrm%20dt%7D%3D-ae%5E%7B-t%7D)
![\dfrac{\mathrm d^2y_p}{\mathrm dt^2}=ae^{-t}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y_p%7D%7B%5Cmathrm%20dt%5E2%7D%3Dae%5E%7B-t%7D)
Substituting these into the ODE gives
![ae^{-t}-6ae^{-t}+9ae^{-t}=4ae^{-t}=4e^{-t}\implies a=1](https://tex.z-dn.net/?f=ae%5E%7B-t%7D-6ae%5E%7B-t%7D%2B9ae%5E%7B-t%7D%3D4ae%5E%7B-t%7D%3D4e%5E%7B-t%7D%5Cimplies%20a%3D1)
so that the particular solution is
![\boxed{y(t)=C_1e^{-3t}+C_2te^{-3t}+e^{-t}}](https://tex.z-dn.net/?f=%5Cboxed%7By%28t%29%3DC_1e%5E%7B-3t%7D%2BC_2te%5E%7B-3t%7D%2Be%5E%7B-t%7D%7D)
They met after a/(x/20) = (3/5x)/(x/20) = 12 mins.
Answer
y=1/2x-5
Step-by-step explanation:
any line with a 1/2 must be parallel also it cannot be the same line or they wont be parallel
Answer:
What im guessing is that you translate the mixed fractions into regular fractions or even whole numbers. so translate the largest and shortest and i guess thats how you do it?