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Home » SMP Unlocked: What This Minecraft Acronym Actually Means (Don’t Miss!) - go-checkin.com

SMP Unlocked: What This Minecraft Acronym Actually Means (Don’t Miss!) - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 inom{5}{3} = 10

📌 Step 2: Count number of trios with exactly 2 close pairs

📌 Therefore, for a fixed trio \( \{A, B, C\} \), suppose \( AB \) and \( BC \) are close, but \( AC \) is not. Then this trio contributes.

📌 So, to count such trios, we count the number of triples where two edges form a path of length 2 (i.e., a "V" shape), and the third edge is absent.

📌 We identify all such "V-shaped" trios in the graph with 5 nodes and 3 close pairs.

📌 Let the 3 close pairs form a path: \( A - B - C \). Then the pairs are \( AB, BC, AC \), with only \( AB \) and \( BC \) close â so 2 close pairs, 1 non-close (namely \( AC \)). This trio counts.

📌 Any other configuration of 3 close pairs that does not form such a path?

📌 Try a star: \( AB, AC, BC \) â but thatâs 3 edges all connected to B â actually forms a triangle. Then every pair is close: 3 close pairs â violates our "exactly 2" condition.

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Now sum them:
\sec^2 x + \csc^2 x + 2\sec x \csc x + 1 + 2\sin x \cos x
Recall that $\sec^2 x = 1 + \tan^2 x$, $\csc^2 x = 1 + \cot^2 x$, but...
\sec^2 x + \csc^2 x = \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} = \frac{...
Also, $\sec x \csc x = \frac{1}{\sin x \cos x}$, so:
2\sec x \csc x = \frac{2}{\sin x \cos x}
And $2\sin x \cos x$ remains.
Let $u = \sin x \cos x$. Since $x \in (0, \frac{\pi}{2})$, $u > 0$, an...
Now rewrite the entire expression in terms of $u$:
\frac{1}{u^2} + \frac{2}{u} + 1 + 2u

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