Answer:
B
Step-by-step explanation:
Area = L * W
L = 12 m
W = 10 m
Area = 12 m * 10 m
Area = 120 m^2
Answer: 1 true 2 false
Step-by-step explanation: Sorry I’m kinda rusty if you get it wrong
![y'+xy=xy^2\implies y^{-2}y'+xy^{-1}=x](https://tex.z-dn.net/?f=y%27%2Bxy%3Dxy%5E2%5Cimplies%20y%5E%7B-2%7Dy%27%2Bxy%5E%7B-1%7D%3Dx)
Let
![z=y^{-1}](https://tex.z-dn.net/?f=z%3Dy%5E%7B-1%7D)
, so that
![z'=-y^{-2}y'](https://tex.z-dn.net/?f=z%27%3D-y%5E%7B-2%7Dy%27)
. Then the ODE becomes linear in
![z](https://tex.z-dn.net/?f=z)
with
![-z'+xz=x\implies z'-xz=-x](https://tex.z-dn.net/?f=-z%27%2Bxz%3Dx%5Cimplies%20z%27-xz%3D-x)
Find an integrating factor:
![\mu(x)=\exp\left(\displaystyle\int-x\,\mathrm dx\right)=e^{-x^2/2}](https://tex.z-dn.net/?f=%5Cmu%28x%29%3D%5Cexp%5Cleft%28%5Cdisplaystyle%5Cint-x%5C%2C%5Cmathrm%20dx%5Cright%29%3De%5E%7B-x%5E2%2F2%7D)
Multiply both sides of the ODE by
![\mu](https://tex.z-dn.net/?f=%5Cmu)
:
![e^{-x^2/2}z'-xe^{-x^2/2}z=-xe^{-x^2/2}](https://tex.z-dn.net/?f=e%5E%7B-x%5E2%2F2%7Dz%27-xe%5E%7B-x%5E2%2F2%7Dz%3D-xe%5E%7B-x%5E2%2F2%7D)
The left side can be consolidated as a derivative:
![\left(e^{-x^2/2}z\right)'=-xe^{-x^2/2}](https://tex.z-dn.net/?f=%5Cleft%28e%5E%7B-x%5E2%2F2%7Dz%5Cright%29%27%3D-xe%5E%7B-x%5E2%2F2%7D)
Integrate both sides with respect to
![x](https://tex.z-dn.net/?f=x)
to get
![e^{-x^2/2}z=e^{x^2/2}+C](https://tex.z-dn.net/?f=e%5E%7B-x%5E2%2F2%7Dz%3De%5E%7Bx%5E2%2F2%7D%2BC)
where the right side can be computed with a simple substitution. Then
![z=1+Ce^{x^2/2}](https://tex.z-dn.net/?f=z%3D1%2BCe%5E%7Bx%5E2%2F2%7D)
Back-substitute to solve for
![y](https://tex.z-dn.net/?f=y)
.
Answer:
d = 100 - 25t
Step-by-step explanation: