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Home » A rectangle's diagonal is 10 cm, and one side is 6 cm. What is the area of the rectangle? - ECD Germany

A rectangle's diagonal is 10 cm, and one side is 6 cm. What is the area of the rectangle? - ECD Germany

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 \[x \approx 1.8\]

📌 Therefore, the width of the path is approximately 1.8 meters.

📌 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.

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