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how to find range - Nurtured Nest

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 To find the longest altitude, we use the shortest side, since altitude is inversely proportional to the base. The shortest side is $ 7 $ cm.

📌 h_{ ext{longest}} = rac{2 \cdot 20\sqrt{3}}{7} = rac{40\sqrt{3}}{7} ext{ cm}

📌 Thus, the length of the longest altitude is $ oxed{rac{40\sqrt{3}}{7}} $ cm.Question: A paleobotanist studying fossilized ferns models the growth pattern of a prehistoric plant using the equation $ 4x^2 - 12xy + 9y^2 + 8x - 36y + 20 = 0 $. Determine whether this equation represents a degenerate conic section and, if so, identify the type of degeneracy.

📌 We begin by analyzing the general quadratic form:

📌 Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

📌 Given equation:

📌 4x^2 - 12xy + 9y^2 + 8x - 36y + 20 = 0

📌 Identify coefficients:

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