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Re: Help with Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112384] Re: Help with Solve
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 12 Sep 2010 03:11:20 -0400 (EDT)

eq1 = n*Sin[x] == (m*v^2)/r;

eq2 = n*Cos[x] == m*g;

soln = Simplify[
   Solve[{eq1, eq2}, {x, n}][[{1, -1}]]] //
  Quiet

{{n -> -((m*Sqrt[g^2*r^2 + v^4])/r), 
     x -> -ArcCos[-((g*r)/Sqrt[g^2*r^2 + v^4])]}, 
   {n -> (m*Sqrt[g^2*r^2 + v^4])/r, 
     x -> ArcCos[(g*r)/Sqrt[g^2*r^2 + v^4]]}}

Simplify[{eq1, eq2} /. soln,
 Element[{m, g, r, v}, Reals]]

{{True, True}, {True, True}}


Bob Hanlon

---- Eduardo  Cavazos <wayo.cavazos at gmail.com> wrote: 

=============
On Sep 9, 3:23 am, Eduardo  Cavazos <wayo.cava... at gmail.com> wrote:

> Here's a couple of equations:
>
> eq1 = n*Sin[x] == (m*v^2)/r;
> eq2 = n*Cos[x] == m*g;
>
> The goal is to solve for 'x'.
>
> I can do this in a roundabout way via:
>
>     Solve[eq1 /. Solve[eq2, n], x]

I should point out that the answer that I get from using Solve this
way is:

    {{x -> ArcTan[v^2/(g r)]}}

which is form the answer I'm looking for. :-) Again, I'm just
wondering if Mathematica can do the work for me, instead of having to
manually eliminate 'n' in a separate step.

Sjoerd and Bob recommended using Reduce. Thanks for the tip! I tried
to use Reduce but the results it produced were not in the above form.

Ed



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