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Home » ‘Open Mouth’ Secrets Revealed—Ex periodo of Transformation You Can’t Ignore! - Carbonext

‘Open Mouth’ Secrets Revealed—Ex periodo of Transformation You Can’t Ignore! - Carbonext

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 A company's profit \( P \) in thousands of dollars can be modeled by the quadratic equation \( P(x) = -2x^2 + 12x - 16 \), where \( x \) is the number of units produced in hundreds. How many units should the company produce to maximize profit?

📌 The profit function is a quadratic equation in the form \( ax^2 + bx + c \), where \( a = -2 \), \( b = 12 \).

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

📌 \[ x = -\frac{12}{2 \times (-2)} = \frac{12}{4} = 3 \]

📌 The company should produce 300 units (since \( x \) is in hundreds) to maximize profit.

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

📌 The sum of the first \( n \) terms is \( S_n = 3n^2 + 5n \).

📌 The \( n \)-th term \( a_n \) is given by:

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