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Home » عوض مرة أخرى: \(x = 1.6 + 2 = 3.6\). - Silent Sales Machine

عوض مرة أخرى: \(x = 1.6 + 2 = 3.6\). - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \vec{F} \cdot \vec{r}' = (-3\sin t)(-3\sin t) + (3\cos t)(3\cos t) = 9\sin^2 t + 9\cos^2 t = 9(\sin^2 t + \cos^2 t) = 9

📌 Thus, the integral becomes:

📌 W = \int_0^{2\pi} 9 \, dt = 9 \cdot 2\pi = 18\pi

📌 The work done by the field is:

📌 \boxed{18\pi}

📌 Question:** An electrical engineer studies a alternating current signal modeled by \( z(t) = 4e^{i\omega t} + 3e^{-i\omega t} \), where \( z(t) \) represents voltage in complex form. Compute the maximum real value of \( |z(t)| \).

📌 First, express \( z(t) \) in terms of cosine and sine:

📌 z(t) = 4(\cos \omega t + i\sin \omega t) + 3(\cos \omega t - i\sin \omega t) = (4 + 3)\cos \omega t + i(4 - 3)\sin \omega t

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