Solving for a variable help

  • Thread starter MathiasArendru
  • Start date
  • Tags
    Variable
In summary: Yea no problem but there i can just add 3x^2 to both sides, in my example its v^2t^2 so i can't do the same thing here?In summary, the conversation is about a question regarding the Lorenz factor and its derivation, and the person asking for help is struggling to solve it. The expert summarizer suggests bringing all terms with "t" to one side and the other terms to the other side, isolating t^2, and then taking roots. The person asking for help tries to apply this method but is unsure how to handle the v^2t^2 term. The expert suggests subtracting v^2t^2 from both sides, explaining that it is no
  • #1
MathiasArendru
17
0
Hey guys, this is a little silly question but it bothers me. I am not a math genius (yet i hope) and I am still in elementary school so there's a lot to learn. But i just read about the lorenz factor in this example he basically used pythagoras of this light clock in a train, so it started of as

[tex](ct)^2 = (cx)^2 + (vt)^2[/tex]

and he derived it into:

[tex]t = \frac{x}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

I would have posted an attemp to solve it but i really just don't know how to crack it and get started

Pleeeaaase help it would be really nice :D
 
Last edited:
Mathematics news on Phys.org
  • #2
That is nothing you can derive (at least not in the way you ask for here), that is a definition of γ.
 
  • #3
right its me god I am stupid! he solved for t not gamma don't really know what went through my head while i wrote it. i corrected it in the post now
 
  • #4
OK, I'll help you get started: bring all terms which have a ##t## to one side of the equation and the other terms on the other side. Isolate ##t^2## so you have ##t^2 = \text{something}##. Then take roots.
 
  • #5
ok ill try:

[itex]c^2t^2 = c^2x^2 + v^2t^2[/itex]
[itex]t^2 = \frac{c^2x^2 + v^2t^2}{c^2}[/itex]
Dividing both sides by t^2
[itex]1 = \frac{c^2x^2 + v^2t^2}{c^2t^2}[/itex]

im stuck... lol
normally i don't really have trouble when solving for variables but this one irritates me.. can i have another hint ? :)
 
  • #6
MathiasArendru said:
ok ill try:

[itex]c^2t^2 = c^2x^2 + v^2t^2[/itex]
[itex]t^2 = \frac{c^2x^2 + v^2t^2}{c^2}[/itex]

I can see a ##t^2## on the LHS and on the RHS. The idea is to have all occurences of ##t^2## on the LHS.
 
  • #7
Exacly that's the though part, because normally i would just divide out the t^2 but that won't help in this example as it would leave me with a 1 on the LHS.. and that wouldn't help much,, is there some mechanism or method that i am missing that could solve this? i feel like there's something i haven't learned that could allow this to be solved.. or is it just me that's blind?
 
  • #8
MathiasArendru said:
Exacly that's the though part, because normally i would just divide out the t^2 but that won't help in this example as it would leave me with a 1 on the LHS.. and that wouldn't help much,, is there some mechanism or method that i am missing that could solve this? i feel like there's something i haven't learned that could allow this to be solved.. or is it just me that's blind?

If you have ##2x^2 = 5 - 3x^2##, can you solve that? You just need to do the same thing here. Isolate ##x##.
 
  • #9
Yea no problem but there i can just add 3x^2 to both sides, in my example its [itex]v^2t^2[/itex] so i can't do the same thing here?
 
  • #10
MathiasArendru said:
Yea no problem but there i can just add 3x^2 to both sides, in my example its [itex]v^2t^2[/itex] so i can't do the same thing here?

You could try subtracting ##v^2t^2## from both sides.
 
  • #11
MathiasArendru said:
Yea no problem but there i can just add 3x^2 to both sides, in my example its [itex]v^2t^2[/itex] so i can't do the same thing here?

Why do you think v2 is different from 3?
 

1. How do I solve for a variable in an equation?

To solve for a variable in an equation, you need to isolate the variable on one side of the equal sign. This can be done by using inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same number.

2. Can you give an example of solving for a variable?

Sure, let's say we have the equation 3x + 5 = 17. To solve for x, we need to get rid of the 5 on the left side of the equal sign. We can do this by subtracting 5 from both sides, giving us 3x = 12. Then, we divide both sides by 3, and we get the solution x = 4.

3. What is the order of operations when solving for a variable?

The order of operations when solving for a variable is the same as when solving any other equation. You should first simplify any expressions inside parentheses, then do any operations involving exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

4. What should I do if the variable is on both sides of the equation?

If the variable appears on both sides of the equation, you should first try to simplify the equation as much as possible. Then, use inverse operations to move all terms with the variable to one side of the equation. Once the variable is isolated, you can solve for it as usual.

5. Are there any special cases when solving for a variable?

Yes, there are a few special cases when solving for a variable. For example, if the equation contains fractions, you may need to multiply both sides by the lowest common denominator to eliminate them. If the equation contains absolute value, you may need to consider both the positive and negative solutions. Additionally, if the equation contains logarithms or exponential functions, you may need to use logarithmic or exponential properties to solve for the variable.

Similar threads

Replies
4
Views
1K
Replies
1
Views
695
Replies
1
Views
1K
  • Calculus
Replies
29
Views
513
  • Differential Equations
Replies
15
Views
2K
  • General Math
Replies
4
Views
999
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Mechanics
Replies
30
Views
760
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
  • General Math
Replies
5
Views
1K
Back
Top