Step-by-step explanation:
This sales tax table (also known as a sales tax chart or sales tax schedule) lists the amount of sales tax due on purchases between $0.00 and $59.70 for a 5% sales tax rate.
...
5% Sales Tax Chart ($0.00 - $59.70)
Price 20.10
Tax 1.01
Price 30.10
Tax 2.01
Tax 2.51
In the smaller triangle, let
be the length of the smallest leg. Then the smallest leg in the larger triangle is
.
Within the scope of the smaller triangle, we have
such that

Then within the larger the triangle, we would have

Now we can solve for
:


Substitute

, so that

![\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%5D%3D-%5Cdfrac1%7Bx%5E2%7D%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%2B%5Cdfrac1x%5Cleft%28%5Cdfrac1x%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D%5Cright%29%3D%5Cdfrac1%7Bx%5E2%7D%5Cleft%28%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dz%5E2%7D-%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dz%7D%5Cright%29)
Then the ODE becomes


which has the characteristic equation

with roots at

. This means the characteristic solution for

is

and in terms of

, this is

From the given initial conditions, we find


so the particular solution to the IVP is
Answer:
Please give me the rest of the question
Step-by-step explanation:
I will answer you in the comments.
:D