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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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