Tony Soprano has a collection of five-dollar and one-dollar bilis in his shirt pocket. He has 100 bills in all worth a total of
1 answer:
Answer:
Step-by-step explanation:
From the question we are told that:
Five-dollar bill x
One-dollar bill y
Total number of bills
Worth of bills
Generally the equation for Total number of bills is mathematically given by
Since it is made up of five and one dollar bills
Therefore
Hence the Equation for Total worth of bills is
The System of equations used is
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This ODE is linear in
, and you can already contract the left hand side as the derivative of a product:
![\dfrac{\mathrm d}{\mathrm dt}\left[5y\sin t\right]=\cos t\sin^2t](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5B5y%5Csin%20t%5Cright%5D%3D%5Ccos%20t%5Csin%5E2t)
Integrating both sides with respect to
yields
Given that
, we have
so that the particular solution over the interval is
This ODE is linear in
Integrating both sides with respect to
Given that
so that the particular solution over the interval is