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5/2*pi
this post was submitted on 25 May 2025
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Bottle, Hamburger, Ale
B+B+B=30 B+H+H=20 H+A+A=9
B=20-2H
20-2H+20-2H+20-2H=30
60-6H=30
60-30=6H
30/6=H
H=5
B=10
5+2A=9
2A=9-5
2A=4
A=4/2
A=2
intermediate Result: H=5 B=10 A=2
(H+H-B) -> inf 0 -> inf integral of (((B sin(D))/ (A D))dD
Simplifying
0 -> inf integral of B/A (sin(D)/D)dD
It is known that 0->inf of (sin(x)/x)dx is equal to π/2 Then (10/2)(π/2)
Final Result: 5π/2
Sorry for the formatting, I don't know how to fix it
I am amazed at how convoluted your way to solve the first three equations is, but I applaud you for pulling through and solving the integral. That's where I chickened out, because I'd have had to look something up.
It's mainly the formatting and I wanted to "prove" it. It is easy to see that the bottles are 10 because 3B=30, so I was showing off. The integral I did have to look it up because I was thinking it was not converging as sin(x) never does. But then got distracted with a video of a guy doing the Feynman technique for the sin(x)/x part. So I just summarize it as "it is known..."
Did not expect so many people to solve this. I love lemmy.
I started solving it then opened the comments to start writing down my work, then saw someone else solved it so I stopped