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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 05:12:24
|
I know there is a conventional way to do this, but i'm really interested in another method: How do you do this task with the lagrangian algorithm?
What sidelength does a box with the sidelength of x, y, z and minimal surface have, when the top side doesnt exist? The Volume V0 ist constant.
Any help is appreciated 🙂 I know how to do it with 2 variables but it becomes somewhat complicated fast for more than 2? Can i cross out some variables somehow?
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 05:13:42
|
When i'm trying the determinant version, it obviously is dependant from 3 instead of 2 variables. That way i get the equation 2z^2(x-y)
Which leads to z=0
And x=y
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 05:14:25
|
but this just erases everything in the equation V_0=xyz
And z=0 is obviously not a real solution
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 05:28:15
|
i found this video for it, if anyone is interested. I didnt finish it yet, but i thought someone might be interested
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 05:28:16
|
https://www.youtube.com/watch?v=nDuS5uQ7-lo
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:04:02
|
ok i'm still not sure, if i'm able to solve it 😅
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:04:53
|
the way he does it, he gets some neat solutions for each equation, but that doesnt work for my problem that well. Since the best equation i get is x+y=0
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:04:56
|
but that cant be]
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:20:26
|
Wait shouldn't this be "or x=y"
| 0 | 1 | 196,376,941,891,158,000 |
Arne
|
4134
|
Arne
| false |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:20:51
|
yes!
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:21:11
|
sorry, i'm not used to using the logical and and or operators yet 😄
| 0 | 1 | null | null | null | null | null |
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:21:20
|
Which means you can ignore the z=0 part and define z using V_0
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:23:19
|
the problem is, that V_0 would be dependant on z then
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:23:37
|
z would be dependent on V_0
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:23:41
|
Not the other way right
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:23:49
|
Since V_0 is constant
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:25:17
|
yep. But if i try to solve for z in this case, i'm not able to separate it from v_0, so that cannot be the solution at that point
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:25:20
|
Anyway, I'd be helpful if you showed your working
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:25:42
|
Also you need to realise that the solution might depend on V_0
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:26:19
|
This guy got solutions as numbers because he doesn't seem to have a constant like V_0
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:42:10
|
he got the constant 1
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:42:23
|
which can be treated the same way
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:42:41
|
i know the solution depends on v_0 but i dont seem to find the lagrangian way 😄
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:43:09
|
^
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:43:43
|
Also I'm not sure this implies you knew the solution depended on v_0
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:45:16
|
ok this is really hard to translate i guess
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:46:07
|
so... i know the solution is
$$\sqrt[3]{2V_0} = x = y, \frac{1}{2}\sqrt[3]{2v_0}$$
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 510,789,298,321,096,700 |
TeXit
|
01/16/2022 06:47:21
|
**Arne**
|
196376941891158016.png
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:48:18
|
That looks plausible
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:48:43
|
so the x, y, z are dependant on $V_0$. But i got equations like
$$\frac{V}{2}+4\sqrt{Vz} = A$$
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:48:56
|
which doesnt help me at all 😅
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:49:13
|
Ok which face are you "missing"
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 510,789,298,321,096,700 |
TeXit
|
01/16/2022 06:49:18
|
**Arne**
|
196376941891158016.png
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:50:18
|
Constraint: V = xyz
Minimise: xy+2yz+2xz
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:50:23
|
Does that sound right
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:50:25
|
yup
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:50:38
|
btw. thanks for your patience with me 😄
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:51:23
|
So taking the x part:
y+2z = lambda*yz
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:51:49
|
Y part:
x+2z = lambda* xz
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:52:30
|
And z part:
2(x+y) = lambda* xy
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:52:47
|
yup, i got the same
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:53:20
|
so lambda can be $\frac{y+2z}{yz}$ and the equivalent for every other equation
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 510,789,298,321,096,700 |
TeXit
|
01/16/2022 06:53:23
|
**Arne**
|
196376941891158016.png
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:53:43
|
I'm thinking of manipulating it slightly differently
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:53:52
|
except for 2(x+y) another possible solution there is x=0 and y=0
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:55:19
|
hm.. i might be wrong on that one... i've tried a couple of different approaches now 😄
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:55:33
|
Hmm how about subtracting the first 2:
y-x = lambda * z (y-x)
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:55:33
|
my paperwork is confusing (can you say that in english?)
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:55:44
|
I get what you mean
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:56:06
|
Oh yea i did that like yesterday or so! (but at that point i didnt take the derivative of z for some reason)
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:56:11
|
So we have 2 cases:
1. Lambda = 1/z
Or 2. X=y
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:56:32
|
I'll just do 1 first
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:56:42
|
that's how i got $2z^2(x-y)=0$
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 510,789,298,321,096,700 |
TeXit
|
01/16/2022 06:56:45
|
**Arne**
|
196376941891158016.png
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:57:06
|
Ok so if lambda*z = 1
| 0 | 1 | null | null | null | null | null |
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89 |
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|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:57:19
|
And you put it into the 1st equation
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:57:28
|
You get z=0
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:57:35
|
Which is obviously wrong
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:57:41
|
So case 1 can't happen
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:57:52
|
Hence x=y
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:58:15
|
You get the same with this
| 0 | 1 | 510,789,298,321,096,700 |
TeXit
|
0796
|
TeXit
| true |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:58:25
|
Since we know none of the side lengths are 0
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:58:34
|
yup! but at that point i got stuck...
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:58:45
|
You get this now right?
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 06:59:17
|
Totally, like i said, i got to this point with multiple approaches (since it's no different from lagrangians with 2 variables)
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 06:59:43
|
Nice, now let's let x=y=k so that we can replace all the x and y with k
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:00:13
|
k+2z = lambda * kz
4k = lambda * k^2
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:00:38
|
And V = k^2*z
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:01:00
|
Now we can easily solve from here, I assume
| 0 | 1 | null | null | null | null | null |
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89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:01:37
|
(k+2z)/(kz) = 4/k
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:01:48
|
k+2z = 4z
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:01:58
|
And z = k/2
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:02:11
|
Now V = k^3/2
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:02:19
|
And we can get k from this
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:02:27
|
Which gives x, y and z
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 07:03:59
|
awesome!! thank you so much 😄
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:04:27
|
Np, Lagrange multipliers is a very cool tool to have
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 07:04:33
|
i really got stuck at this point and couldnt find an answer (for days actually... i've always tried it again with a different approach to get to this point again)
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 07:04:49
|
this seems so easy when you see the solution 😅
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:05:08
|
It happens sometimes
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:05:15
|
Especially if you've tried it a lot
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 714,483,444,394,229,900 |
Frosty_
|
01/16/2022 07:05:32
|
Try to restart again with a clear mind so you don't go down the same path again
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 07:05:55
|
thanks again! 🙂
| 0 | 1 | null | null | null | null | null |
|||||
89 |
help-10
|
bac8edccad674791bdf920378e0bee9e
| 196,376,941,891,158,000 |
Arne
|
01/16/2022 07:05:57
|
.close
| 0 | 1 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 08:15:37
|
Adsz.png
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 08:15:49
|
I don't understand the third line
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 08:16:01
|
third fourth and the rest
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 08:16:15
|
how do we derive it for theta?
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 08:16:45
|
like when we take the derivative of f_x for theta what do we get?
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 08:31:02
|
@Helpers
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 869,532,694,688,706,600 |
EpsilonNought
|
01/16/2022 09:29:09
|
What language is this
| 0 | 1 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 869,532,694,688,706,600 |
EpsilonNought
|
01/16/2022 09:29:15
|
I don’t understand
| 0 | 1 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 09:29:26
|
it just asks
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 09:29:44
|
$\pdv{f}{\theta*r}$
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 510,789,298,321,096,700 |
TeXit
|
01/16/2022 09:29:47
|
**Cüneyt**
|
886679767145918525.png
| 0 | 1 | null | null | null | null | null |
||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 09:29:55
|
I couldn't type it but
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 09:29:59
|
you got it
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 869,532,694,688,706,600 |
EpsilonNought
|
01/16/2022 09:30:05
|
Ok yeh
| 0 | 1 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 886,679,767,145,918,500 |
June8
|
01/16/2022 09:30:10
|
relations are given as you see
| 1 | 0 | null | null | null | null | null |
|||||
90 |
help-10
|
850c51b4d5d84951be67609a1c52e527
| 869,532,694,688,706,600 |
EpsilonNought
|
01/16/2022 09:30:16
|
I see
| 0 | 1 | null | null | null | null | null |
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