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Re: Help with Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112337] Re: Help with Solve
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 10 Sep 2010 04:47:24 -0400 (EDT)

Use Reduce

eq1 = n*Sin[x] == (m*v^2)/r;
eq2 = n*Cos[x] == m*g;

cons = {m > 0, g > 0, r > 0, v > 0};

sys = Join[{eq1, eq2}, cons];

FullSimplify[Reduce[sys, x, Reals], cons] // ToRadicals

Element[C[1], Integers] && 
   v == -((n^2*r^2 - g^2*m^2*r^2)^(1/4)/Sqrt[m]) && 
   ((x == 2*(Pi*C[1] + ArcTan[
                  Sqrt[1 - (2*g*m)/(g*m + n)]]) && n > g*m) || 
      (2*ArcTan[Sqrt[1 - (2*g*m)/(g*m + n)]] + x == 
           2*Pi*C[1] && g*m + n < 0))


Bob Hanlon

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

=============
Hello!

A newb question I'm sure... :-)

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.e. solve eq2 for 'n', substitute this into eq1, and solve the result
for 'x'. But this approach seems too "manual".

Is there a more straightforward way to carry out the problem? I tried
this:

    Solve[{eq1, eq2}, x]

but it doesn't seem to work. What's a good way to go about this?

Thanks!

Ed



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