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Home » Therefore, the radius of the sphere is 6 units. - Appcentric

Therefore, the radius of the sphere is 6 units. - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Für eine Einheitseingabe \( u(t) = 1 \) im steady-state nähert sich \( \frac{dy}{dt} \approx 0 \).

📌 Also \( 0 + 4y = 2 \times 1 \).

📌 Löse nach \( y \): \( 4y = 2 \) → \( y = \frac{2}{4} = 0.5 \).

📌 ### Frage 5

📌 Ein Umweltingenieur modelliert die Konzentration \( C \) eines Schadstoffs in einem See als \( C(t) = C_0 e^{-kt} \), wobei \( C_0 = 100 \) mg/L, \( k = 0.05 \) Tag\(^{-1}\), und \( t \) in Tagen gemessen wird. Wie lange dauert es, bis die Konzentration unter 10 mg/L fällt?

📌 Stelle die Ungleichung auf: \( 100 e^{-0.05t} < 10 \).

📌 Teile beide Seiten durch 100: \( e^{-0.05t} < 0.1 \).

📌 Nimm den natürlichen Logarithmus: \( -0.05t < \ln(0.1) \).

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