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Home » From Silence to Stardom: How PKSM Captured Millions in a Week—Give It Up! - Carbonext

From Silence to Stardom: How PKSM Captured Millions in a Week—Give It Up! - Carbonext

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 7d \equiv 0 \pmod{12}

📌 This means \( 12 \mid 7d \). Since \( \gcd(7, 12) = 1 \), 12 must divide \( d \). Thus, the smallest such \( d \) is:

📌 After 12 days, the total displacement is \( 7 \times 12 = 84 \equiv 0 \pmod{12} \), returning to the starting segment.

📌 Therefore, the participant returns to segment 1 after:

📌 Question:** An environmental scientist models soil compaction using the vector field \( \vec{F}(x, y) = \langle -y, x \rangle \), representing rotational stress. Find the work done by this field along the circular path \( \vec{r}(t) = \langle 3\cos t, 3\sin t \rangle \) for \( t \in [0, 2\pi] \).

📌 The work is given by the line integral:

📌 W = \int_C \vec{F} \cdot d\vec{r}

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