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Home » $ \sin(-8\pi/9) = -\sin(40^\circ) $ - Rice University

$ \sin(-8\pi/9) = -\sin(40^\circ) $ - Rice University

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Sorted: 1.38, 1.45, 1.45, 1.52, 1.55, 1.60

📌 Sum = 1.45+1.45+1.52+1.55 = <<1.45+1.45+1.52+1.55=6.0>>6.0

📌 A microgrid researcher models wind turbine output, which peaks at 12 hours with 8.4 MW and drops linearly to 2.4 MW over the next 10 hours. The solar array produces a steady 5.1 MW for 16 hours. If the total daily demand is 200 MWh, and turbines run fully during peak, what is the net energy surplus or deficit assuming no battery storage beyond 24-hour cycle?

📌 Turbine output: Triangle from 12 to 22 hrs (10 hrs), peak 8.4 MW

📌 Total generation = 42 + 81.6 = <<42+81.6=123.6>>123.6 MWh

📌 A microgrid researcher designs a battery system to store excess hydroelectric energy. The system can charge at 12 MW for 5 hours daily. On average, 7 hours of the day require power draw of 6 MW. If the system supplies 90% of night demand from storage, what is the minimum storage capacity needed in MWh?

📌 Sorted data: 2.3, 2.6, 2.7, 3.0, 3.1, 3.2, 3.4, 3.7

📌 Q1 (median of first half): median of 2.3,2.6,2.7 = 2.6

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