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Home » Freemind Mind Mapping Software Free Download - Sourci

Freemind Mind Mapping Software Free Download - Sourci

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 لـ $k = 1$:

📌 z = 210^\circ, \quad z = 240^\circ

📌 لـ $k = 2$، تتجاوز الزوايا $360^\circ$. لذلك، الحلول هي:

📌 z = 30^\circ, 60^\circ, 210^\circ, 240^\circ

📌 30^\circ + 60^\circ + 210^\circ + 240^\circ = 540^\circ

📌 إذن، مجموع جميع الزوايا $z$ التي تحقق $\sin(2z) = \frac{\sqrt{3}}{2}$ هو $\boxed{540^\circ}$.

📌 السؤال: أوجد إحداثيات الرأس الرابع لهرم رباعي منتظم إذا كانت ثلاثة من رؤوسه تقع في النقاط $(0,0,0)$ و $(a,a,0)$ و $(0,a,a)$، حيث $a$ عدد صحيح موجب، وجميع الإحداثيات أعداد صحيحة.

📌 الحل: لنجعل رؤوس الهرم الرباعي المنتظم هي $A = (0,0,0)$ و $B = (a,a,0)$ و $C = (0,a,a)$. لإيجاد إحداثيات الرأس الرابع $D = (x,y,z)$، نستخدم خصائص الهرم الرباعي المنتظم، حيث تكون جميع الحواف متساوية في الطول. طول الحافة $s$ يُعطى بالمسافة بين $A$ و $B$:

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