Answer:
12x=9+5x^{2}
12x=9+5x2
Step-by-step explanation:
Answer:
30 Gallons
Step-by-step explanation:
Okay so you need to start by making an equation for yourself. Since the container starts at 1/10 of the total, you want to start by saying 1/10x. Then you add 12 gallons of water to make it half full. So 1/10x + 12 = 1/2x where x is the total amount that can fit in the container.
1/10x + 12 = 1/2x (Move your x's to the same side.)
12 = 1/2x - 1/10x (Find a common denominator.)
12 = 5/10x - 1/10x (Simplify/)
12 = 4/10x (Multiply both sides by 10; your demoninator)
120 = 4x (Divide)
x = 30
Your container holds 30 gallons.
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Answer:
Step-by-step explanation:
Given
![\int {\ln(u)} \, du = u[\ln(u) - f(u)] + c](https://tex.z-dn.net/?f=%5Cint%20%7B%5Cln%28u%29%7D%20%5C%2C%20du%20%3D%20u%5B%5Cln%28u%29%20-%20f%28u%29%5D%20%2B%20c)
Required
Find f(u)
To do this, we start by integrating the left-hand side
Using integration by parts, we have:
So, we have:
Differentiate
Integrate
So:
So, we have:
Integrate du using constant rule
Subtract c from both sides
Subtract u ln(u) from both sides
Rewrite as:
