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Home » Sei \( u = \sin \theta \). Die Gleichung wird zu: - Network4

Sei \( u = \sin \theta \). Die Gleichung wird zu: - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 a - x + z = a \quad \Rightarrow \quad z = x

📌 نعوض $z = x$ و $y = a - x$ في $x^2 + y^2 + z^2 = 2a^2$:

📌 x^2 + (a - x)^2 + x^2 = 2a^2 \quad \Rightarrow \quad x^2 + a^2 - 2ax + x^2 + x^2 = 2a^2 \quad \Rightarrow \quad 3x^2 - 2ax + a^2 = 2a^2 \quad \Rightarrow \quad 3x^2 - 2ax - a^2 = 0

📌 x = \frac{2a \pm \sqrt{4a^2 + 12a^2}}{6} = \frac{2a \pm 4a}{6} \quad \Rightarrow \quad x = a \quad \text{أو} \quad x = -\frac{a}{3}

📌 بما أن $x$ يجب أن يكون عددًا صحيحًا، فإن $x = a$، وبالتالي $y = 0$ و $z = a$. لذلك، إحداثيات الرأس الرابع هي:

📌 \boxed{(a, 0, a)}

📌 السؤال: أوجد القيمة القصوى للتعبير $(\sin x + \cos x)^2

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\( \binom{8}{2} = \frac{8 \times 7}{2} = 28 \)
Solution:** Start: 1 atm at surface.
Each 100 m multiplies pressure by 1.1.
We solve: \( 1 \times (1.1)^n = 1000 \) → \( (1.1)^n = 1000 \)
Take log: \( n = \log_{1.1}(1000) = \frac{\log 1000}{\log 1.1} = \frac...
So depth: \( 72.45 \times 100 \approx 7245 \) meters (round to nearest...
At 7200 m: \( (1.1)^{72} \approx 999.9 \) → just below
At 7300 m: \( (1.1)^{73} \approx 1099.9 \) → exceeds
So it reaches 1000 atm during ascent at ~7300 meters. But question ask...
Since 72.45 × 100 = 7245, check:

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