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V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
February 9, 2013
Solved

Real and positive root needed

  • February 9, 2013
  • 5 replies
  • 32418 views

How can I gat a Real and positive root - see the picture and attach (Mathcad 15 and, pardon, Mathcad Prime 2.0)

SolveRealPositiv.png

Best answer by ValeryOchkov

But the best solution is from Mathcad - a complex of symbolic and numeric math:

2%D0%B2-%D0%9A%D0%BE%D0%BD%D1%83%D1%81%D0%9F%D0%BE%D0%BB%D1%83%D1%81%D1%84%D0%B5%D1%80%D0%B0.png

5 replies

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Werner_E25-Diamond I
25-Diamond I
February 9, 2013

First thought was to use the modifier "assume,ALL>0", but the result is going crazy that way and i don't know why - sorry. You can only see it in the Prime version, as 15 say that the result is too big to display.

Maybe the conditions you see in doing so help you - they didn't help me understanding the problem.

At least you get a single result with "assume, ALL>0" if you assign V a value before solving.

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
February 9, 2013

Thanks, but it is not a solution. I need in the answer V not m.

W
Werner_E25-Diamond I
25-Diamond I
February 9, 2013

Valery Ochkov schrieb:

Thanks, but it is not a solution. I need in the answer V not m.

Yes , I've seen that you used the generiv V to proof that the ratio r/h is sqrt(2). But then in this case it should be clear that this ratio is not dependent on the value of V.

W
Werner_E25-Diamond I
25-Diamond I
February 9, 2013

This is really a tough one (with/for Mathcad).

You have to simplify the problem by hand from the order 12 down to an order three equation to make it work - Blame on you Mathcad!

coneerror.png

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
February 9, 2013

Thanks, Werner. I can do it "by hand" but I would like to do it by Mathcad for others same problems.

ConeEngHand.png

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
February 9, 2013

Or

ConeEngHand-2.png

A
AlanStevens19-Tanzanite
19-Tanzanite
February 9, 2013

How about the following? It often helps to get rid of square roots! Still a little convoluted though!

Alan

rsol.PNG

Actually, you don't need to square f to get the above solution. I should have inserted a 'simplify' after f^2 to make it obvious (if it wasn't already!) that substituting r6 for r^6 is a sensible thing to do.

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
February 9, 2013

Thanks!

Cylinder d = h

Cylinder without top r = h

Cone without top h/r = sqr(2)

Cone with top h/r = 2*sqr(2)

And what about symbolic solution of this problem:

Cone-Shere.png

And what about symbolic solution (R/H -? H/L-?) of this problem:

http://communities.ptc.com/videos/2239

H
HarveyHensley12-Amethyst
12-Amethyst
February 17, 2013

Reformulate the problem to find the ratio, not r. See attached and the figure below.

cone.png

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    February 17, 2013

    Thanks, Harvey!

    For a cone - no problem. A problem is/was for a cone and a semisphere or cone and a part of sphere:

    http://communities.ptc.com/servlet/JiveServlet/downloadImage/2-196854-45139/267-257/Cone-Shere.png

    H
    HarveyHensley12-Amethyst
    12-Amethyst
    February 17, 2013

    Valery,

    Is the problem to minimize the surface to volume ratio of the hemisphere+cone? If that is the case, then the answer is for the h/r ratio to be 0. The sphere has less area/vol than the conical shape.

    In your numerical example, you have specified the volume. In my attached worksheet I have given an example with h specified. Note that the plot of the surface/vol ratio increases with h.r = h/r. Also note that the derivative of the surface/vol rate never goes to zero. Thus, the symbolic solve can't find a solution.

    V
    24-Ruby IV
    ValeryOchkov24-Ruby IVAuthor
    24-Ruby IV
    March 21, 2016

    An article about this problem

    http://twt.mpei.ac.ru/ochkov/hybrid.pdf

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