Re: Equation problem
- To: mathgroup at smc.vnet.net
- Subject: [mg42220] Re: [mg42206] Equation problem
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Tue, 24 Jun 2003 01:27:06 -0400 (EDT)
- References: <200306230949.FAA12500@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Dan wrote:
>
> I need to solve the system of equations (in Mathematica notation):
>
> r1 == 0.0298
> r2 == 0.0335
> n == Abs[(r2-r1)/T]
> 2*Pi*Sum[r1+i*T, {i,0,n}] == 10
> T>0
>
> I tried (ignoring T>0) to use NSolve, which didn't work. I guessed the
> problem is that the summation limit depends on T which is also a part of the
> summand. However, Mathematica succefully solves the simpler Sum[n, {i, 0,
> n}] == 2. What is the essence of the problem? How can I solve it?
Depending on what exactly you did, this may not be appropriate
Mathematica notation. One way to get a solution is to set up as below.
r1 = 0.0298;
r2 = 0.0335;
n = Abs[(r2-r1)/tt];
Now we may solve it.
In[7]:= Select[NSolve[2*Pi*Sum[r1+i*tt, {i,0,n}] == 10, tt], (tt/.#)>0&]
Solve::ifun: Inverse functions are being used by Solve, so some
solutions may
not be found.
Out[7]= {{tt -> 0.0000750721}}
For purposes of getting a positive solution it would probably make more
sense to do as follows.
In[13]:= n = (r2-r1)/tt;
In[14]:= NSolve[2*Pi*Sum[r1+i*tt, {i,0,n}] == 10, tt]
Out[14]= {{tt -> 0.0000750721}}
Daniel Lichtblau
Wolfram Research
- References:
- Equation problem
- From: "Dan" <gentlemanjack@casino.com>
- Equation problem