# Recent content by The Chaz

1. ### Can logarithms be applied to Modular arithmetic

I'm not sure of your background with modular arithmetic, so I'll just start small... We consider all numbers with the same remainder after dividing by n to be EQUIVALENT. For example, 2 = 5 = 8 = 11 = 300000000000002 = -1 mod 3. (Here, the "triple" bar sign would be better than the double bar...
2. ### System of coupled masses and springs homework

(From an organizational standpoint, you could probably pick a more descriptive title...)
3. ### Trigonometric Equations find all solutions

sec(3t) = 2 invert (flip) both sides cos(3t) = 1/2 Get a unit circle. Each point is of the form (cosine(angle), sine(angle)) We want the angles where cosine is 1/2. These angles are: π/3 and 5π/3 But since we have 3t, we include all solutions less than 6π. See the above reply for more details...

Have you ever seen P = e^{rt} before? Usually, I would recommend exponential growth/decay for bacteria situations. Furthermore, "Doubling" and "halving" are very closely related!
5. ### Instructor doesn't know the answer to his own exam!

What was the question (...in question, so to speak)?
6. ### Unique abelian group of order n

Since this was the first hit when I Googled my homework, I'll resurrect this thread with my thoughts. This holds trivially for prime numbers. Claim: For n "square-free", \mathbb{Z}_n is (up to isomorphism) the unique abelian group of order n. We extend the fact that \mathbb{Z}_{ab} \cong...
7. ### What is the absolute value of imaginary numbers, why not supernatural numbers?

That is the beauty of math?!?! I wish someone had told me earlier... :cool:
8. ### What is the absolute value of imaginary numbers, why not supernatural numbers?

I guess so! There was another "seemingly active thread" about closed form expressions that caught my eye today, as did the fact that some first-poster had resurrected it after years of inactivity...
9. ### Partition Function p(n)

Too bad this guy doesn't come around anymore... I was just starting to like him! But seriously, forks. I do NOT know of a closed-form equation.
10. ### Differentiation of fraction

Cancel a factor of h from top and bottom. Then let h -> 0 and you'll get \frac{-2}{x^2+2x+1} = \frac{-2}{(x + 1)^2} Later, when you learn "shortcuts" (i.e rules of differentiation that will be proven), this second form will look a lot more familiar.
11. ### Other answers to 1+1=2

1 Point for calling out the flagrant bump. + 1 point for referencing the thread at the same time = the new constant named in your honor - "M"
12. ### Calculate arcsin(sin√5)

TsAmE, I might add that Calculus *methods* are not appropriate for this problem (even though it might appear in a calc book/course). This is more about, as Mark44 has mentioned, coterminal angles and the domain of inverse trig functions. Some people have an easier time working with degrees at...
13. ### Help with Algebra

Yeah, super disappointing. After finding critical points, you could use a sign chart to determine which are maxima and which are minima
14. ### Statistical probability to help with a crime

Maybe you should invite the employees to a poker game...?!?!
15. ### Volume computation (from cross-sectional area)

a. the base of the square isn't (y^2); it's (3-y^2).