CURED - 2024-11-06

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SmokeDetector

07:17

[ SmokeDetector | MS ] Bad keyword with email in body, potentially bad ns for domain in body, potentially bad keyword in body (62): Achieve NEET Success with Alpha NEET Academy: Top Reasons to Enroll Today‭ by Alpha Kanchi‭ on math.SE

8 hours later…

Sahaj

15:44

hi everyone

Q: Range of the function $\frac{x^4 + y^4 + z^4}{(x + y + z)^4}$ for $x,y,z>0$ such that $(x+y+z)^3 = 32xyz$

The question is: $x$, $y$, and $z$ are positive reals. If $(x+y+z)^3 = 32xyz$, then find the numerical range of $$f(x,y,z)=\frac{x^4 + y^4 + z^4}{(x + y + z)^4}.$$ Since all terms involved are positive, I realize the function is at least greater than $0$. Since the denominator is greater than the...

functions

dupe

Feeds

16:43

Q: What is the maximum and the minimum of Cs?

Definition : $C_s = \{ n \in \mathbb{N} \mid n \text{ reaches 1 in exactly } s \text{ steps in the Collatz sequence, and } n \neq 2^s \}.$ For instance, we have: $C_5 = \{5\}, \\ C_6 = \{10\}, \\ C_7 = \{3, 20, 21\}, \\ C_8 = \{6, 40, 42\}, \\ C_9 = \{12, 13, 80, 84, 85\}, \\ C_{10} = \{24, 26, 1...