the radius = 3.14*2r= 6.28r.i got this answer from user
Lizplllllllll
Its a rectangle so two sides are equal and both sides that are opposite of each other are equal. So two sides are 37. Then you add them together to get 74, then subtract it from 164 to get 90 the rest of the fence length. Then divide it by two to get 45 which is the other side lengths, so it would be a 37 by 45 rectangle one side would be 37 while the other two are 45.
8 dollars per hour because 92-20=72. That the allowance you earn per week. After that you divide 72/9 because you work 9 hours to get to 72 dollars.
Your solution seems fine. What does the rest of the error message say?
![\displaystyle y^{1/2}\frac{\mathrm dy}{\mathrm dx} + y^{3/2} = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%5E%7B1%2F2%7D%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%20%2B%20y%5E%7B3%2F2%7D%20%3D%201)
Substitute
![z(x)=y(x)^{3/2} \implies \dfrac{\mathrm dz}{\mathrm dx}=\dfrac32y(x)^{1/2}\dfrac{\mathrm dy}{\mathrm dx}](https://tex.z-dn.net/?f=z%28x%29%3Dy%28x%29%5E%7B3%2F2%7D%20%5Cimplies%20%5Cdfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dx%7D%3D%5Cdfrac32y%28x%29%5E%7B1%2F2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D)
to transform the ODE to a linear one in <em>z</em> :
![\displaystyle \frac23\frac{\mathrm dz}{\mathrm dx} + z = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac23%5Cfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dx%7D%20%2B%20z%20%3D%201)
Divide both sides by 2/3 :
![\displaystyle \frac{\mathrm dz}{\mathrm dx} + \frac32z = \frac32](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dx%7D%20%2B%20%5Cfrac32z%20%3D%20%5Cfrac32)
Multiply both sides by the integrating factor,
:
![\displaystyle e^{3x/2}\frac{\mathrm dz}{\mathrm dx} + \frac32 e^{3x/2}z = \frac32 e^{3x/2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20e%5E%7B3x%2F2%7D%5Cfrac%7B%5Cmathrm%20dz%7D%7B%5Cmathrm%20dx%7D%20%2B%20%5Cfrac32%20e%5E%7B3x%2F2%7Dz%20%3D%20%5Cfrac32%20e%5E%7B3x%2F2%7D)
Condense the left side into the derivative of a product :
![\displaystyle \frac{\mathrm d}{\mathrm dx}\left[e^{3x/2}z\right] = \frac32 e^{3x/2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5Be%5E%7B3x%2F2%7Dz%5Cright%5D%20%3D%20%5Cfrac32%20e%5E%7B3x%2F2%7D)
Integrate both sides and solve for <em>z</em> :
![\displaystyle e^{3x/2}z = \frac32 \int e^{3x/2}\,\mathrm dx \\\\ e^{3x/2}z = e^{3x/2} + C \\\\ z = 1 + Ce^{-3x/2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20e%5E%7B3x%2F2%7Dz%20%3D%20%5Cfrac32%20%5Cint%20e%5E%7B3x%2F2%7D%5C%2C%5Cmathrm%20dx%20%5C%5C%5C%5C%20e%5E%7B3x%2F2%7Dz%20%3D%20e%5E%7B3x%2F2%7D%20%2B%20C%20%5C%5C%5C%5C%20z%20%3D%201%20%2B%20Ce%5E%7B-3x%2F2%7D)
Solve in terms of <em>y</em> :
![y^{3/2} = 1 + Ce^{-3x/2}](https://tex.z-dn.net/?f=y%5E%7B3%2F2%7D%20%3D%201%20%2B%20Ce%5E%7B-3x%2F2%7D)
Given that <em>y</em> (0) = 16, we have
![16^{3/2} = 1 + Ce^0 \implies C = 16^{3/2}-1 = 63](https://tex.z-dn.net/?f=16%5E%7B3%2F2%7D%20%3D%201%20%2B%20Ce%5E0%20%5Cimplies%20C%20%3D%2016%5E%7B3%2F2%7D-1%20%3D%2063)
so that the particular solution is
![\boxed{y^{3/2} = 1 + 63e^{-3x/2}}](https://tex.z-dn.net/?f=%5Cboxed%7By%5E%7B3%2F2%7D%20%3D%201%20%2B%2063e%5E%7B-3x%2F2%7D%7D)