Mastering Equation Solving: 3 Ways to Simplify Complex Equations

  • Context: Undergrad 
  • Thread starter Thread starter yoyochan
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Discussion Overview

The discussion revolves around solving a set of complex equations simultaneously, with a focus on potential methods for simplification and solution strategies. Participants explore the origins of the equations and the possibility of using matrices for solving them.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related

Main Points Raised

  • One participant presents a series of equations involving variables x, y, z, and a time variable t, questioning their simultaneous solvability.
  • Another participant expresses confusion about the equations, particularly noting the identical right-hand sides (RHS) of two equations and asks for clarification on their origin.
  • Some participants suggest that matrices could be a viable method for solving the equations, although this is not universally accepted.
  • There is curiosity about any additional constraints that may apply to the solutions of the equations.
  • One participant encourages the original poster to demonstrate prior attempts at solving the equations to facilitate further assistance from others.
  • There is a suggestion to use Wolfram Alpha for finding solutions if the primary interest is in obtaining answers rather than understanding the derivation.

Areas of Agreement / Disagreement

Participants express uncertainty about the equations and their origins, and there is no consensus on the best method for solving them. Multiple approaches are suggested, but the discussion remains unresolved regarding the most effective strategy.

Contextual Notes

Participants note the potential for additional constraints on the solutions, but these constraints are not specified. The discussion also highlights the need for clarity on the equations' origins, which remains unaddressed.

Who May Find This Useful

This discussion may be of interest to those looking for methods to solve complex equations, particularly in the context of simultaneous equations and matrix applications.

yoyochan
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(3*10^8 t - 19288.47)^2 = (x-18167.44)^2 + (y-38037.28)^2 + (z-433.35)^2
(3*10^8 t - 17862.46)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2
(3*10^8 t - 69656.18)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2
(3*10^8 t - 14143.42)^2 = (x-24729.37)^2 + (y-34126.78)^2 + (z-930.27)^2
 
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yoyochan said:
(3*10^8 t - 19288.47)^2 = (x-18167.44)^2 + (y-38037.28)^2 + (z-433.35)^2
(3*10^8 t - 17862.46)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2[/color]
(3*10^8 t - 69656.18)^2 = (x-40607.42)^2 + (y-11317.32)^2 + (z-5.077)^2[/color]
(3*10^8 t - 14143.42)^2 = (x-24729.37)^2 + (y-34126.78)^2 + (z-930.27)^2
You are wanting to solve these simultaneously? Where did these come from?

Are you sure the RHS of two lines is supposed to be identical?
 
It is strange equations..
But I think you can do it by matrices ..
Can't you!
 
Maged Saeed said:
It is strange equations..
That's why I'm curious to know where they arose.

Are there any other constraints on the solutions?

But I think you can do it by matrices ..
Have you looked into this, and tried solving by any means? Others are more inclined to offer help if they can see you have at least made some attempt at solving it by your own effort.

Do you have in mind how many sig figs you would like in the answers?

If all you are interested in are the solutions, have you tried wolfram alpha?
 

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