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24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
May 17, 2019
Question

Need help with symbolic calculation

  • May 17, 2019
  • 2 replies
  • 2566 views

I have got the solution for the V function, but I cannot have got the solution for the V2 function!

Help please!

The Mathcad Prime 5 sheet in attach! 

The problem.
We take a round workpiece and cut a sector out of it.
We then fold the cone from the workpiece.

The question is what is value of the cutting angle at which the volume of the cone will be maximum.

I solved the problem with one cone analytically, but I cannot solve it analytically for two cones!

V.png

2 replies

L
LucMeekes23-Emerald IV
23-Emerald IV
May 17, 2019

Maybe this helps:

LM_2019017_SymbolicSolve.png

The numeric solve (using root() ) shows one resul that looks very much like it is pi... See attached.

Success!

Luc

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    May 17, 2019

    Thanks, Luc!

    But see Mathcad 15

    Sym15.png

    W
    Werner_E25-Diamond I
    25-Diamond I
    May 17, 2019

    Its too demanding for the symbolics.

    Even Wolfram returns a numeric result only (apart from local minimum pi) - at least with just standard computation time:

    link to uncle wolfram

    B.PNG

    B2.PNG

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    May 17, 2019

    I find old solution from my coauthor Victor Korobov - only Mathcad 11!

    Can you do it in Mathcad 15?

    3_04a_2_Bucket_Symbol.gif

    W
    Werner_E25-Diamond I
    25-Diamond I
    May 17, 2019
    @ValeryOchkov wrote:

    I find old solution from my coauthor Victor Korobov - only Mathcad 11!

    Can you do it in Mathcad 15?

     

    Here you are. A simple assume statement does the trick and, Heureka!, you also get the symbolic solution!!!

    The assume statement itself is ignored (we also get solutions greater than 2 pi) and there is a somewhat strange behavior of the result when it comes to plotting (using the values for the vertical markers) which makes necessary a redefinition of alpha.opt which I don't understand.

    B.PNG

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