Bright entertainment trends with youth appeal.
How do I simplify $\tan(\alpha-\beta)$ into $\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$? I tried: $$\tan(\alpha-\beta) = \\\frac{\sin(\alpha-\bet...
In a game with two equal teams, the home team wins any game with probability $p>\frac12$. In a best of three playoff series, a team with a home advanta...
Q&A for people studying math at any level and professionals in related fields
By using a sieve created by Prime Number Tables set up by the formula PN+(PNx6) for numbers generated by 6n+or-1, takes 182 calculations to identify 170 c...
Problem statement: There are 1000 coins. 999 coins have heads and tails. 1 coin is unfair and both sides are heads. You choose a coin at random and toss i...
Given $a'>a,b>0$ and $f$ concave, show that $f(a+b)-f(a)\geq f(a'+b)-f(a')$. Can anyone give me a hint on how to show that inequality...
Find $y''$ if $x^4 + y^4 = 16$ by implicit differentiation So after the first implicit differentiation I got this equation (let's call it A...
Let $A = [a_{ij}] \in \mathbb{K}^{n \times n}$, where $\mathbb{K} = \mathbb{R}$ or $\mathbb{K} = \mathbb{C}$. In the case $\mathbb{K} = \mathbb{C}$, for e...
The question speaks for itself, since the question comes from a contest environment, one where the use of calculators is obviously not allowed, can anyone...
Q&A for people studying math at any level and professionals in related fields
