Answer:
![v=\sqrt{\frac{E}{m}}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7BE%7D%7Bm%7D%7D)
Step-by-step explanation:
The formula is given as:
![E=mv^2](https://tex.z-dn.net/?f=E%3Dmv%5E2)
We need to solve this formula for v, that means that v to one side and let it be solved in terms of the other variables (E and m). First, we isolate v:
![E=mv^2\\\frac{E}{m}=\frac{mv^2}{m}\\\frac{E}{m}=v^2](https://tex.z-dn.net/?f=E%3Dmv%5E2%5C%5C%5Cfrac%7BE%7D%7Bm%7D%3D%5Cfrac%7Bmv%5E2%7D%7Bm%7D%5C%5C%5Cfrac%7BE%7D%7Bm%7D%3Dv%5E2)
To isolate v, and eliminate the "square", we need to take square roots of both sides, that will give us v in terms of the other variables:
![\frac{E}{m}=v^2\\\sqrt{\frac{E}{m}}=\sqrt{v^2}\\\sqrt{\frac{E}{m}}=v](https://tex.z-dn.net/?f=%5Cfrac%7BE%7D%7Bm%7D%3Dv%5E2%5C%5C%5Csqrt%7B%5Cfrac%7BE%7D%7Bm%7D%7D%3D%5Csqrt%7Bv%5E2%7D%5C%5C%5Csqrt%7B%5Cfrac%7BE%7D%7Bm%7D%7D%3Dv)
Putting v to left side (convention), we finally have:
![v=\sqrt{\frac{E}{m}}](https://tex.z-dn.net/?f=v%3D%5Csqrt%7B%5Cfrac%7BE%7D%7Bm%7D%7D)
X + (x + 10) = 154
2 x + 10 = 154
2 x = 154-10 = 144
x = 72 (ans)
Not sure if it’s right
Step-by-step explanation:
-7(-3r+2)=3r-6
Distribute the - 7
21r-14=3r-6
Add 14
21r=3r+8
Subtract 3r
18r=8
Divide 18r by 8
2.25 should be the answer to r.
Answer:
There will be 200 000 bacteria after 8 hours
Step-by-step explanation:
The crop quadruples every hour.
x represents the number of hours that pass after preparing the crop
y represents the number of bacteria after x hours.
The equation for y in function of x 3 hours after observing the crop is:
![y = 192(4^{x - 3})](https://tex.z-dn.net/?f=y%20%3D%20192%284%5E%7Bx%20-%203%7D%29)
We want to know after how long there will be 200 000 bacteria.
Then we make y = 200 000 and clear x.
![200\ 000 = 192(4^{x - 3})\\\\log(200\ 000) = log(192(4^{x-3}))\\\\log(200\ 000) = log(192) + log(4 ^{x-3})\\\\log(200\ 000) - log(192) = (x-3)log(4)\\\\\frac{log(200\ 000) - log(192)}{log(4)} = (x-3)\\\\x = 3 + \frac{log(200\ 000) - log(192)}{log(4)}\\\\x = 8\ hours](https://tex.z-dn.net/?f=200%5C%20000%20%3D%20192%284%5E%7Bx%20-%203%7D%29%5C%5C%5C%5Clog%28200%5C%20000%29%20%3D%20log%28192%284%5E%7Bx-3%7D%29%29%5C%5C%5C%5Clog%28200%5C%20000%29%20%3D%20log%28192%29%20%2B%20log%284%20%5E%7Bx-3%7D%29%5C%5C%5C%5Clog%28200%5C%20000%29%20-%20log%28192%29%20%3D%20%28x-3%29log%284%29%5C%5C%5C%5C%5Cfrac%7Blog%28200%5C%20000%29%20-%20log%28192%29%7D%7Blog%284%29%7D%20%3D%20%28x-3%29%5C%5C%5C%5Cx%20%3D%203%20%2B%20%5Cfrac%7Blog%28200%5C%20000%29%20-%20log%28192%29%7D%7Blog%284%29%7D%5C%5C%5C%5Cx%20%3D%208%5C%20hours)
Answer:
y=4x+10
Step-by-step explanation:
2y-8x-20=0
2y-8x=0+20
2y-8x=20
2y=8x+20
y=4x+10
Hope that will help!!