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,-2. place the x as 8 and y as -2.
Answer:
![60+10x=6](https://tex.z-dn.net/?f=60%2B10x%3D6)
Step-by-step explanation:
Hi there!
![4+\displaystyle \frac{2}{3} x=\frac{2}{5}](https://tex.z-dn.net/?f=4%2B%5Cdisplaystyle%20%5Cfrac%7B2%7D%7B3%7D%20x%3D%5Cfrac%7B2%7D%7B5%7D)
To get rid of the fraction
, multiply both sides of the equation by 3 (the denominator):
![3(4+\displaystyle \frac{2}{3} x)=3(\frac{2}{5})\\\\3*4+\frac{3*2}{3}x =\frac{3*2}{5} \\\\12+2x =\frac{6}{5}](https://tex.z-dn.net/?f=3%284%2B%5Cdisplaystyle%20%5Cfrac%7B2%7D%7B3%7D%20x%29%3D3%28%5Cfrac%7B2%7D%7B5%7D%29%5C%5C%5C%5C3%2A4%2B%5Cfrac%7B3%2A2%7D%7B3%7Dx%20%3D%5Cfrac%7B3%2A2%7D%7B5%7D%20%5C%5C%5C%5C12%2B2x%20%3D%5Cfrac%7B6%7D%7B5%7D)
To get rid of the fraction
, multiply both sides of the equation by 5 (the denominator):
![\displaystyle 5(12+2x) =5(\frac{6}{5})\\\\5*12+5*2x=\frac{5*6}{5} \\\\60+10x=6](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%2812%2B2x%29%20%3D5%28%5Cfrac%7B6%7D%7B5%7D%29%5C%5C%5C%5C5%2A12%2B5%2A2x%3D%5Cfrac%7B5%2A6%7D%7B5%7D%20%5C%5C%5C%5C60%2B10x%3D6)
I hope this helps!
Sorry bro idkhdjdjjdjdjdjfjfjxjj83848 89**%%
Thanks with all of my heart!
ik im not first but have a lovely day! u are really kind! never forget that!