Solving a quiz problem with basic math

[nyu]

This isn't homework, but I missed the last few classes so I'm in dire need of help. I was given a quiz today, amazingly - I was able to do all of it with just basic math knowledge...except one >_> And it's bothering me that I don't understand it >_>

Here is the problem:

[URL][PLAIN]http://www.fall3n.com/homework/solvev.gif[/PLAIN]

[PLAIN]http://www.fall3n.com/homework/solvev.gif[/PLAIN]

If anybody could explain it thoroughly, it'd be appreciated ;)
Thank you!

 

[Tide]

I assume that's a radical in the denominator.

Multiply both sides by the radical, square both sides then solve for v.

 

[Tom McCurdy]

Ok um I am assuming the equation is $$t=T/(1-(V^2/c^2))$$

therefore

t = T*v^2
-------
v^2-c^2
therefore
v=-c sqroot(t)
-----------
sqroot(t-T)

 

[Tom McCurdy]

Alright I kind of cheated and used the calculator last time
but I solved by hand and got the following

$$t=\frac{T}{{1 - v^2/c^2}}$$

$$t=\frac{Tc^2}{{c^2-v^2}}$$
$$c^2-v^2=\frac{Tc^2}{{t}}$$
$$-v^2=\frac{Tc^2}{{t}}-c^2$$
$$v^2=\frac{-Tc^2}{{t}}+\frac{c^2t}{{t}}$$
$$v^2=\frac{tc^2-Tc^2}{{t}}$$
$$v^2=\frac{c^2(t-T)}{{t}}$$
$$v=+ or - \frac{c\sqrt{(t-T)}}{{t}}$$

 

[Tom McCurdy]

I am very tired though and could have made a mistake please check your answers with someone else or have someone confirm mine

 

[HallsofIvy]

Yes, Tom McCurdy's last response:

$$v=+ or - \frac{c\sqrt{(t-T)}}{{t}}$$

is correct.

 

[Tom McCurdy]

YES... not only did i do some algerbra but I learned latex