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Home » \(S_9 = 3(9)^2 + 5(9) = 243 + 45 = 288\). - Nelissen Grade advocaten

\(S_9 = 3(9)^2 + 5(9) = 243 + 45 = 288\). - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 r^2 \leq \frac{100}{1} = 100 \Rightarrow r \leq 10.

📌 But we must check if this maximum is **attainable**. That is, does there exist a $\theta$ such that $\sin(2\theta) = 1$ and $r = 10$?

📌 Set $\sin(2\theta) = 1 \Rightarrow 2\theta = \frac{\pi}{2} + 2k\pi \Rightarrow \theta = \frac{\pi}{4} + k\pi$.

📌 Try $\theta = \frac{\pi}{4}$:

📌 Then $r^2 = \frac{100}{1} = 100 \Rightarrow r = 10$.

📌 Check if this point lies within the circular region:

📌 The circle has radius 10, so $r = 10$ is on the boundary — valid.

📌 Thus, the **maximum possible value of $r$** is:

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