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Home » Perimeter = \(2(\textlength + \textwidth) = 48\) - RoadRUNNER Motorcycle Touring & Travel Magazine

Perimeter = \(2(\textlength + \textwidth) = 48\) - RoadRUNNER Motorcycle Touring & Travel Magazine

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Maximum occurs when:

📌 \frac{\pi}{6}t + \phi = \frac{\pi}{2} \Rightarrow t = \frac{6}{\pi} \left( \frac{\pi}{2} - \phi \right) = \frac{6}{\pi} \left( \frac{\pi}{2} - 1.287 \right)

📌 t \approx \frac{6}{\pi} (1.571 - 1.287) = \frac{6}{\pi} (0.284) \approx 0.54 \text{ months}

📌 So the maximum water level is $ \boxed{25} $, and it first occurs approximately $ \boxed{0.54} $ months after the start of the year, or around early January.

📌 Question: A disaster response team models the periodic power grid stability using the function $ p(t) = 9\cos\left(\frac{\pi}{12}t\right) + 12\sin\left(\frac{\pi}{12}t\right) $. What is the amplitude and the phase shift $ \phi $ in the equivalent form $ R\cos\left(\frac{\pi}{12}t - \phi\right) $?

📌 We compute the amplitude:

📌 R = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15

📌 To find the phase shift:

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