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Home » 5Frage: Berechne \(\cos 150^\circ\). - Databee Business Systems

5Frage: Berechne \(\cos 150^\circ\). - Databee Business Systems

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 \( P(-800) = P_0 \cdot e^{(\ln 2 / 200)(-800)} = P_0 \cdot e^{-4\ln 2} = P_0 \cdot (e^{\ln 2})^{-4} = P_0 \cdot 2^{-4} = P_0 / 16 \)

📌 Given that current count (1000 years ago, t = 0) is 48, so \( P_0 = 48 \) (at t = 0 for layer A)

📌 But that’s the modern value. We want the count 600 years ago, i.e., at t = -600

📌 So: \( P(-600) = 48 \cdot e^{(\ln 2 / 200)(-600)} = 48 \cdot e^{-3\ln 2} = 48 \cdot 2^{-3} = 48 / 8 = 6 \)

📌 A hydrologist models the discharge of a river as a function of rainfall: \( Q = 50R^{0.7} \), where \( Q \) is discharge in m³/s and \( R \) is rainfall in cm. If rainfall increases from 30 cm to 40 cm, by how much does discharge increase? Round to the nearest whole number.

📌 Initial discharge: \( Q_1 = 50 \cdot 30^{0.7} \)

📌 \( 30^{0.7} = e^{0.7 \ln 30} \approx e^{0.7 \cdot 3.4012} = e^{2.3808} \approx 10.81 \)

📌 \( Q_1 = 50 \cdot 10.81 = 540.5 \)

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