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Home » Thus, $ E(t) = t^2 $. - Red Crowns

Thus, $ E(t) = t^2 $. - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Question: Compute $\cos 180^\circ + \cot 30^\circ$.

📌 Solution: $\cos 180^\circ = -1$, and $\cot 30^\circ = \frac{1}{\tan 30^\circ} = \frac{1}{\frac{\sqrt{3}}{3}} = \sqrt{3}$. Therefore:

📌 \cos 180^\circ + \cot 30^\circ = -1 + \sqrt{3}

📌 \boxed{-1 + \sqrt{3}}

📌 $$**Question:** A philosopher of science is pondering the nature of cyclical patterns in scientific discovery. They note that certain patterns repeat every few years, akin to modular arithmetic cycles. What is the remainder when $12345 + 12347 + 12349 + 12351$ is divided by 6?

📌 To find the remainder of $12345 + 12347 + 12349 + 12351$ when divided by 6, we first compute each term modulo 6:

📌 \equiv 3 \pmod{6}

📌 \equiv 5 \pmod{6}

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