Answer: 4 gallons = 15 liters, 8 liters = 2 gallons, 12.5 liters = 3 gallons, and 6 gallons = 23 liters.
The answer is A
Explanation
60 + 3x = 180 ( linear pair)
3x = 180 - 60
3x = 60
x = 60/3
x = 20
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I think the answer would be A because 5% ×100=0.05 , and in the question they have been telling us that it decreased by 5 from the last week so the equation would be g of the last week - 0.05
Answer:
![P=M(1-e^{-kt})](https://tex.z-dn.net/?f=P%3DM%281-e%5E%7B-kt%7D%29)
Step-by-step explanation:
The relation between the variables is given by
![\frac{dP}{dt} = k(M- P)](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%20%3D%20k%28M-%20P%29)
This is a separable differential equation. Rearranging terms:
![\frac{dP}{(M- P)} = kdt](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7B%28M-%20P%29%7D%20%3D%20kdt)
Multiplying by -1
![\frac{dP}{(P- M)} = -kdt](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7B%28P-%20M%29%7D%20%3D%20-kdt)
Integrating
![ln(P-M)=-kt+D](https://tex.z-dn.net/?f=ln%28P-M%29%3D-kt%2BD)
Where D is a constant. Applying expoentials
![P-M=e^{-kt+D}=Ce^{-kt}](https://tex.z-dn.net/?f=P-M%3De%5E%7B-kt%2BD%7D%3DCe%5E%7B-kt%7D)
Where
, another constant
Solving for P
![P=M+Ce^{-kt}](https://tex.z-dn.net/?f=P%3DM%2BCe%5E%7B-kt%7D)
With the initial condition P=0 when t=0
![0=M+Ce^{-k(0)}](https://tex.z-dn.net/?f=0%3DM%2BCe%5E%7B-k%280%29%7D)
We get C=-M. The final expression for P is
![P=M-Me^{-kt}](https://tex.z-dn.net/?f=P%3DM-Me%5E%7B-kt%7D)
![P=M(1-e^{-kt})](https://tex.z-dn.net/?f=P%3DM%281-e%5E%7B-kt%7D%29)
Keywords: performance , learning , skill , training , differential equation