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all ben 10 aliens - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \[ \sqrt{2} \cos(c) = 1 \quad \Rightarrow \quad \cos(c) = \frac{1}{\sqrt{2}} \]

📌 These values correspond to \( c = -\frac{\pi}{4} \) (since \(\sin(c) = -\frac{1}{\sqrt{2}}\) and \(\cos(c) = \frac{1}{\sqrt{2}}\)).

📌 Find \( b \):

📌 The period of the function is \( \frac{2\pi}{b} \). Since \( f\left(\frac{\pi}{2b}\right) = 4 \), it indicates a quarter-period shift, consistent with \( b \) being arbitrary for simplicity. Assume one full cycle completes in \( \frac{2\pi}{b} = 2\pi \), giving \( b = 1 \).

📌 Thus, the constants are:

📌 \[\boxed{a = \sqrt{2}, \, b = 1, \, c = -\frac{\pi}{4}, \, d = 3}\]

📌 A virologist researching antiviral therapies models viral load dynamics with the function \( V(t) = V_0 \cos^2(\omega t + \phi) \), where \( V_0 \) is the maximum viral load, \( \omega \) is the angular frequency, and \( \phi \) is the phase shift. If \( V(0) = \frac{V_0}{2} \) and \( V\left(\frac{\pi}{2\omega}\right) = 0 \), find \( \phi \).

📌 The function is given by:

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