[?] Solve this equation with Solve?

Questions
1

Hello everyone. My Name is Karl and at the Moment i try to learn mathematica, but i have some Problems solving an equation.
I want to solve this:
Unbenannt.PNG

First, i want an Expression for m =………, then I want to use this Expression and use the given values for Tx = 68.4, T9=25.4, T1=90, L=0.35 and x=0.05. My Code Looks like this:
Formel.PNG

                   ;If I use STRG C to copy the Right solution it Looks like:

kpiert.PNG

First Question is: What means this " ` " Symbol in the copied stuff infront of the T9 or the L?! Once i had this symbol and because of this the solution was false. For what is this " 1. " ?
Second Question is: when i type all the values dircetly in the Solve line like this:
gelöst.PNG
I get those two values but i guess they are wrong! If I check it with my normal Calculator it should be ~8.22. Also a friend of mine used another Programm and got the value of About 8.22.
I hope you can help me and explain me where my mistakes are. Thanks a lot :wink:

2

What means this " ` " Symbol ?

Is a numeric value with MachinePrecision see for more info.

With correct syntax:

  $Version
   (* "12.0.0 for Microsoft Windows (64-bit) (April 6, 2019)" *)

 
 ClearAll["Global`*"]
 Tx = 68.4; T9 = 25.4; T1 = 90; L = 0.35; x = 0.05;
 NSolve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
 (*{{m -> -8.22068}, {m -> 8.22068}}*)


 Solve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
 {{m -> -8.22068}, {m -> 8.22068}}

Solve gives a error message because Solve command works better with exact values.

ClearAll["Global`*"]
Tx = 684/10; T9 = 254/10; T1 = 90; L = 35/100; x = 5/100;
Solve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
%//N
(*{{m -> -8.22068}, {m -> 8.22068}}*)

 ClearAll["Global`*"]
  Solve[(Tx - T9)/(T1 - T9) == Cosh[m (L - x)]/Cosh[m L], m, Reals]
 (*General solution is impossible*)
3

Thanks for your Answer.
I tried it with your Code but it doesnt work for me.

Fehler123.PNG
Fehler123.PNG601×119 4.52 KB

Any idea what i made wrong again? Do you have also an idea what i Need to type in to get an Expression for m =…… with variables so that i have an General Expression.

4

For me works fine,I tried in Mathematica version 10.2 and 12.0.

5

Ah okay well i have Mathematica 7.0 :wink: Maybe this is the Problem.
Thank you a lot for your Help and time :slight_smile: