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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? | 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 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 | 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 05:14:25 | but this just erases everything in the equation V_0=xyz
And z=0 is obviously not a real solution | 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 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 | 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 05:28:16 | https://www.youtube.com/watch?v=nDuS5uQ7-lo | 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 06:04:02 | ok i'm still not sure, if i'm able to solve it 😅 | 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 06:04:53 | 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 | 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 06:04:56 | 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 | help-10 | 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 | 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 06:23:19 | the problem is, that V_0 would be dependant on z then | 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 06:23:37 | 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 | 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 06:23:49 | 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 | 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 06:25:42 | 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 | 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 06:46:07 | 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 | help-10 | 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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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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