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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 E_1^3 + E_2^3 = 1728 - 3(32)(12) = 1728 - 1152 = 576

📌 Thus, the value is \(\boxed{576}\).

📌 Question: An entrepreneur developing AI for sustainable agriculture models crop yield \( Y \) (in kg) as a function of water input \( x \) (in liters) with \( Y = -2x^2 + 24x + 100 \). What is the maximum possible yield?

📌 The function \( Y = -2x^2 + 24x + 100 \) is a quadratic in standard form, opening downward (since coefficient of \( x^2 \) is negative), so the maximum occurs at the vertex.

📌 The vertex of a parabola \( ax^2 + bx + c \) is at \( x = -\frac{b}{2a} \).

📌 Here, \( a = -2 \), \( b = 24 \), so:

📌 x = -\frac{24}{2(-2)} = \frac{24}{4} = 6

📌 Substitute \( x = 6 \) into the equation:

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