Answer:
V' = -0.11552 *V\\= -0.11552(1.8)\\ \\=-0.20794 million per year
Step-by-step explanation:
Given that oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 3 million barrels of oil in the well; six years later 1,500,000 barrels remain.
i.e. if V stands for volume of oil, then
![V' =kV\\dv/V= kdt\\ln V = kt+C\\V = Ae^{kt}](https://tex.z-dn.net/?f=V%27%20%3DkV%5C%5Cdv%2FV%3D%20kdt%5C%5Cln%20V%20%3D%20kt%2BC%5C%5CV%20%3D%20Ae%5E%7Bkt%7D)
To find A and k
V(0) = A = 3 million
Hence V = ![3e^{kt}](https://tex.z-dn.net/?f=3e%5E%7Bkt%7D)
V(6) = 1.5
i.e. ![1.5 = 3e^{6k}\\ln 1.5 =ln 3 +6k\\k = -0.11552](https://tex.z-dn.net/?f=1.5%20%3D%203e%5E%7B6k%7D%5C%5Cln%201.5%20%3Dln%203%20%2B6k%5C%5Ck%20%3D%20-0.11552)
![V(t) = 3e^{-0.11552t}](https://tex.z-dn.net/?f=V%28t%29%20%3D%203e%5E%7B-0.11552t%7D)
a) Using the above value of k , we have
million per year.
-12=4(x-7)-8x
One solution was found :
x = -4
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-12-(4*(x-7)-8*x)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
-12 - (4 • (x - 7) - 8x) = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
4x + 16 = 4 • (x + 4)
Equation at the end of step 3 :
4 • (x + 4) = 0
Step 4 :
Equations which are never true :
4.1 Solve : 4 = 0
Hope this helps you, Have a nice day.
Answer:
6x, 2x + 4, 5y + 11
Step-by-step explanation:
x + x + x + 2x + x = 6x
(x + 2) + (x + 2) = 2x + 4
y + y + y + y + 10 + y + 1 = 5y + 11
If you divide 12.5 by 25 you should get 0.5
correct answer should be 0.5
Answer:
The weight of the object is 3 kg.
Step-by-step explanation:
<u>Step 1:
</u>
Let object weight be x kg.
Now, as per the available data,
3/4 kg + 3/4 (x kg) = x kg
<u>Step 2:
</u>
3/4 (1 + x) = x
1 + x = 4x/3
1 = x (4/3 - 1)
x = 1 / (1/3)
x = 3
Weight of Object is 3 kg.
<u>Step 3:
</u>
Let's check if this value satisfies the first equation.
3/4 + 3/4 x 3 = 3/4 + 9/4 = 12/4 = 3
Hence proved.