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Home » Thus, one bead costs $ \boxed\frac6919 $ gold coins. - AMAZONAWS

Thus, one bead costs $ \boxed\frac6919 $ gold coins. - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 A company’s profit in thousands of dollars is modeled by \( P(x) = -2x^2 + 20x - 30 \), where \( x \) is the number of units sold in hundreds. What is the maximum profit, and how many units maximize it?

📌 This is a quadratic function in vertex form. The vertex occurs at \( x = -\frac{b}{2a} = -\frac{20}{2(-2)} = 5 \).

📌 So maximum profit occurs when \( x = 5 \), i.e., 500 units.

📌 Plug into \( P(x) \): \( P(5) = -2(25) + 20(5) - 30 = -50 + 100 - 30 = 20 \).

📌 Thus, maximum profit is $20,000.

📌 #### Maximum profit: $20,000 at 500 units

📌 The sum of the first \( n \) terms of an arithmetic sequence is \( S_n = 3n^2 + 5n \). Find the 10th term.

📌 The \( n \)-th term is \( a_n = S_n - S_{n-1} \).

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