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Home » Number of parts in process at once: \( \fracT\Delta t = \frac8.51.25 = 6.8 \). - AMAZONAWS

Number of parts in process at once: \( \fracT\Delta t = \frac8.51.25 = 6.8 \). - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 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:

📌 \tan\phi = \frac{12}{9} = \frac{4}{3} \Rightarrow \phi = \arctan\left(\frac{4}{3}\right) \approx 0.9273 \text{ radians}

📌 So the function can be written as:

📌 p(t) = 15\cos\left(\frac{\pi}{12}t - 0.9273\right)

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