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Home » \Rightarrow L^3 = 0 \Rightarrow L = 0 - Blask

\Rightarrow L^3 = 0 \Rightarrow L = 0 - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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

📌 Here, \( a = -2, b = 40 \)

📌 \( x = -\frac{40}{2 \times -2} = 10 \) (i.e., 1000 units)

📌 Maximum profit: \( P(10) = -2(10)^2 + 40(10) - 150 \)

📌 \( P(10) = -200 + 400 - 150 = 50 \)

📌 Maximum profit is $50,000 at 1000 units.

📌 #### $50,000

📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If the first term is 5 and the common difference is 3, find \( S_{15} \).

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