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
Y=10.55
Z=17.53
Y: tan37=y/14 ; 14(tan37)=10.55
Z: sin53=14/z ; 14/sin53=17.53
Answer: equation = $600 + tx$8 = $640 ; t = 5 additional hours in May
Step-by-step explanation:
Equation = $600 + tx$8/hour = $640
t = ($640 - $600)/$8/hour
t = $40/$8/hour = 5 hours
Answer: Equation = $600 + tx$8 = $640 ; t = 5 additional hours in May
<h2><em>Spymore</em></h2>
This answer to the problem is f (x) =-15/2x^2 + 5x +C
Answer:
B.
Step-by-step explanation: If I know that I need a total of 20 points I start with my greater number. So I start skip counting bu 3. I have to stop skip counting by 3 at 18 or it will go over 20. The remaining amount is 2 that is how many multiple choice questions there are. The I just have to find which sentence equals two.