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\[ k = \frac5411 - \frac4411 \] - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Einsetzen der gegebenen Werte: \( V = 3,14 \times 5^2 \times 10 = 3,14 \times 25 \times 10 = 785 \) Kubikmeter.

📌 Da der Tank zu 75 % gefüllt ist, beträgt das Wasservolumen \( 785 \times 0,75 = 588,75 \) Kubikmeter.

📌 #### 588,75 Kubikmeter

📌 Eine Bakterienpopulation wächst exponentiell und verdoppelt sich alle 3 Stunden. Wenn die anfängliche Population 500 beträgt, wie groß ist die Population nach 12 Stunden?

📌 Die Formel für exponentielles Wachstum lautet \( P = P_0 \times 2^{(t/T)} \), wobei \( P_0 \) die Anfangspopulation, \( t \) die Zeit und \( T \) die Verdopplungszeit ist.

📌 Einsetzen der Werte: \( P = 500 \times 2^{(12/3)} = 500 \times 2^4 = 500 \times 16 = 8000 \).

📌 Ein Ball wird senkrecht nach oben mit einer Anfangsgeschwindigkeit von 20 m/s geworfen. Wie hoch steigt der Ball, bevor er wieder herunterfällt? (Verwenden Sie \( g = 9,8 \, \text{m/s}^2 \) für die Schwerkraft)

📌 Die Formel für die maximale Höhe lautet \( h = \frac{v_0^2}{2g} \).

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