Answer:
![W=2452.5 J](https://tex.z-dn.net/?f=W%3D2452.5%20J)
Step-by-step explanation:
The work is define as the integral of the force times distance. So we have:
![W=\int^{a}_{b}Fxdx](https://tex.z-dn.net/?f=W%3D%5Cint%5E%7Ba%7D_%7Bb%7DFxdx)
Now, we can write the force in terms of density.
![F=m*g=\rho Vg](https://tex.z-dn.net/?f=F%3Dm%2Ag%3D%5Crho%20Vg%20)
V is the volume (V=2*1*1=2 m³)
So the work will be:
![W=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0} 2*1000*9.81*xdx=\int^{0.5}_{0}19620xdx=19620(\frac{x^{2}}{2})|^{0.5}_{0}](https://tex.z-dn.net/?f=W%3D%5Cint%5E%7B0.5%7D_%7B0%7D%202%2A1000%2A9.81%2Axdx%3D%5Cint%5E%7B0.5%7D_%7B0%7D%202%2A1000%2A9.81%2Axdx%3D%5Cint%5E%7B0.5%7D_%7B0%7D19620xdx%3D19620%28%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%29%7C%5E%7B0.5%7D_%7B0%7D)
The limit of integration is between 0 and 0.5 because we want to pump half of the water out of the aquarium.
![W=19620(\frac{x^{2}}{2})|^{0.5}_{0}=19620(\frac{0.5^{2}}{2})](https://tex.z-dn.net/?f=W%3D19620%28%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%29%7C%5E%7B0.5%7D_%7B0%7D%3D19620%28%5Cfrac%7B0.5%5E%7B2%7D%7D%7B2%7D%29)
![W=2452.5 J](https://tex.z-dn.net/?f=W%3D2452.5%20J)
I hope it helps you!
-8 the point on the line with Y=4
Answer:
$665.36
Step-by-step explanation:
2^16 or...
2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2 = 66536 pennies
Answer:
The function is ![P(x) = \frac{1}{2} e^{-x^2} +0.016](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20e%5E%7B-x%5E2%7D%20%2B0.016)
Step-by-step explanation:
From the question we are told that
The rate of growth is
The total profit is
$25,000
The time taken to make the profit is ![x = 2 \ years](https://tex.z-dn.net/?f=x%20%3D%20%202%20%5C%20years)
From the question
is the rate of growth
Now here x represent the time taken
Now the total profit is mathematically represented as
![P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%5Cint%5Climits%20%7BP%27%28x%29%7D%20%5C%2C%20%20%3D%20%20%20%5Cint%5Climits%20%7Bxe%5E%7B-x%5E2%7D%7D%20%5C%2C)
So using substitution method
We have that
![u = - x^2](https://tex.z-dn.net/?f=u%20%3D%20%20-%20x%5E2)
![du = 2xdx](https://tex.z-dn.net/?f=du%20%3D%20%202xdx)
So
![p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%20%5Cint%5Climits%20%7B%5Cfrac%7B1%7D%7B2%7D%20e%5E%7B-u%7D%7D%20%5C%2C%20du)
![p(x) = {\frac{1}{2} [ e^{-u}} +c ]](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%20%7B%5Cfrac%7B1%7D%7B2%7D%20%5B%20e%5E%7B-u%7D%7D%20%2Bc%20%5D)
recall
and let ![\frac{1}{2} c = Z](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20c%20%3D%20%20Z)
At x = 2 years
$25,000
So
Since the profit rate is in million
$25,000 =
$0.025 millon dollars
So
=>
So the profit function becomes
![P(x) = \frac{1}{2} e^{-x^2} +0.016](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20e%5E%7B-x%5E2%7D%20%2B0.016)
Answer: a,b,d,e are all right beacuse they all relate to the question
Step-by-step explanation:
c how ever is no shown on the graph and is therefor wrong