Recent content by SigmaS

The 112 was just arbitrarily determined. I wanted to make $4900^{100}$ easy to calculate by hand. And I'm just trying to solve the probability of the problem, but expressed in much simpler terms. if there's a better way to solve the original problem without modular arithmetic, then that would...

So I was working on solving $(\frac{1}{4900})^{100}$, and I figured the only way to do this neatly is through modular arithmetic. I found that $4900 \equiv 84 \ (\text {mod 112})$, so I concluded $$\frac{1^{100}}{84^{10}\times84^{10} \ (\text{mod 112})}$$ Which should equal...

I was told PEMDAS isn't always followed, particularly in higher level math. Is this true? Because I recall the purpose of PEMDAS is to prevent ambiguity, and without it, at any level, would result in ambiguity, even though it's just a convention and not something we can really prove. Also...

Hey, can you explain why I can rewrite the first equation as (1- n^2)x^2- 2mx+ m^2= 0? It's (1- n^2)x^2 that confuses me. I can complete from there without struggle, but I just don't understand why translating that way works. Also, thank you for the second equation, I finally got the right...

I'm struggling with two particular equations in my Algebra textbook. 1) $x^2+m^2=2mx+(nx)^2 $ 2) $\sqrt{x^2+3x+7}-\sqrt{x^2-3x+9}+2=0$ I know the answer to the first equation is {$\frac{m}{1-n}, \frac{m}{1+n}$}. The answer to the second equation is {$-\frac{9}{5}$}. I don't understand why...