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Home » This Secret to ‘Respect My Authority’ Is Ending Toxic Leadership Forever—Worth Knowing! - DNSFLEX

This Secret to ‘Respect My Authority’ Is Ending Toxic Leadership Forever—Worth Knowing! - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Question: A herpetologist is tracking the movement of a rare frog in a circular region of radius 10 km centered at the origin. The frog’s position is modeled in polar coordinates as $(r, \theta)$, and its path satisfies the equation

📌 r^2 \sin(2\theta) = 100.

📌 Find the maximum possible value of $r$ along this path.

📌 We are given the polar equation:

📌 We want to find the **maximum value of $r$** for which this equation has a solution.

📌 Step 1: Solve for $r^2$:

📌 r^2 = \frac{100}{\sin(2\theta)}.

📌 Since $r^2 \geq 0$, we must have $\sin(2\theta) > 0$. The maximum value of $r^2$ occurs when $\sin(2\theta)$ is minimized (but still positive). The minimum positive value of $\sin(2\theta)$ is approaching 0, but we must consider the domain where the expression is defined and real.

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