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Home » 🎉 Over-the-Top Birthday Balloons Blow Your Party Up—Happy Birthday Magic! - AssociationVoting

🎉 Over-the-Top Birthday Balloons Blow Your Party Up—Happy Birthday Magic! - AssociationVoting

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 \boxed{\left(3, \dfrac{7}{8} \right)}

📌 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 $r^2$:

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