context

1. What does substitute mean in this context?

I was reading a book about special relativity when I saw this blok: (1) s^2 = \Delta x_1^2 + \Delta x_2^2 + \Delta x_3^2 My problem is the substitution of (2a). I don't understand how this substitution looks like or how it works. This question might be stupid or in the wrong forum...
2. Rational Solutions of the tan function in the context of a video game

First of all, I'd like to note that I believe I've already solved the problem I'm about to pose (it just comes down to there being just two rational solutions to the tan function) and as such, am not really in need of help with it. I'm only posting this as a log of a "real-world" application to...
3. L = { $a^nb^mc^n | m \ge n$ } is not context free. With Pumping Lemma through 6 cases

This is the Pumping Lemma for Context Free Languages I refer: And this is the exercise I encounter some problems: $L = \left \{ a^nb^mc^n \mid m \ge n \right \}$ is not context free. Proof- by contradiction using the pumping lemma for context-free languages. Assume that $L$ is...
4. Absolute Value or Cardinality (context question)...

I have this problem: Given the set A = {1, 2, 3, 4, 5}, |P(A)| = I believe this is asking me for the cardinality of the power set P(A). Am I thinking in the right context? Thanks, Joe
5. Simple geometry problem with a complex context

I'm working with 3D geometry, and I've been at this for days. I'm beating my head against a wall, because I'm nearly done with the project. There's only one glitch in my system. The Situation: I have a 3D cartesian coordinate system with a Spherical system overlaid over it (the "poles"...
6. Proof Please: Context Free Grammar

Find context-free grammar for the following languages (with n\geqslant0, m\geqslant0, k\geqslant0). (a) L = \{a^n b^m c^k : n + 2m = k\} What i got so far is: S \to aSc | A A \to bAcc | \lambda (b) L = \{a^n b^m c^k : n = m or m $\not=$ k\} No idea