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Home » B. Wegen’s Gesetz der Gletscherfließgeschwindigkeit - Rice University

B. Wegen’s Gesetz der Gletscherfließgeschwindigkeit - Rice University

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Find common denominator: (7.2d - 5.8d) / (5.8 Ã 7.2) = 10

📌 1.4d = 417.6

📌 d = 417.6 / 1.4 = <<417.6/1.4=298.2857142857143>>298.29 km (rounded to two decimals)

📌 #### 298.29Question: Find the sum of all angles $ z \in [0^\circ, 360^\circ] $ that satisfy $ 2\sin(2z) + 1 = 0 $.

📌 Solution: Solve $ 2\sin(2z) + 1 = 0 \Rightarrow \sin(2z) = -rac{1}{2} $. The general solutions for $ 2z $ are $ 2z = 210^\circ + 360^\circ k $ and $ 2z = 330^\circ + 360^\circ k $, where $ k \in \mathbb{Z} $. Dividing by 2, $ z = 105^\circ, 165^\circ, 285^\circ, 345^\circ $ within $ [0^\circ, 360^\circ] $. The sum is $ 105 + 165 + 285 + 345 = 900^\circ $. oxed{900}

📌 Question: In spherical coordinates, find the equation describing a cone with half-angle $ 60^\circ $ centered along the $ z $-axis.

📌 Solution: A cone with half-angle $ lpha $ in spherical coordinates is defined by $ \phi = lpha $. For $ 60^\circ $, the equation is $ \phi = 60^\circ $. oxed{\phi = 60^\circ}

📌 Question: Find the matrix $ \mathbf{M} $ such that $ \mathbf{M} egin{pmatrix} x \ y \end{pmatrix} = egin{pmatrix} -y \ x \end{pmatrix} $.

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