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Home » Solution: The given equation is $ - High Altitude Science

Solution: The given equation is $ - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 x = rac{-2 \pm \sqrt{4 + 24}}{2} = rac{-2 \pm \sqrt{28}}{2} = rac{-2 \pm 2\sqrt{7}}{2} = -1 \pm \sqrt{7}

📌 The corresponding \(y\)-coordinates are \(y = x + 2\), so:

📌 y = (-1 + \sqrt{7}) + 2 = 1 + \sqrt{7}, \quad y = (-1 - \sqrt{7}) + 2 = 1 - \sqrt{7}

📌 The points of intersection are \(A = (-1 + \sqrt{7}, 1 + \sqrt{7})\) and \(B = (-1 - \sqrt{7}, 1 - \sqrt{7})\).

📌 The area is the area of the circular segment. The central angle \( heta\) subtended by the chord can be found using the dot product of vectors from the origin to the points.

📌 Let \(ec{OA} = \langle -1 + \sqrt{7}, 1 + \sqrt{7}

📌 angle\), \(ec{OB} = \langle -1 - \sqrt{7}, 1 - \sqrt{7}

📌 Dot product:

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