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Home » Average speed: 300 ÷ 6 = 50 mph - Baxtercollege

Average speed: 300 ÷ 6 = 50 mph - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \( a_2 = 3a_1 + 4 = 3 \times 2 + 4 = 10 \)

📌 \( a_3 = 3a_2 + 4 = 3 \times 10 + 4 = 34 \)

📌 \( a_4 = 3a_3 + 4 = 3 \times 34 + 4 = 106 \)

📌 Problem:** A company’s profit \( P \) (in thousands) is modeled by \( P = -2x^2 + 12x - 5 \), where \( x \) is the number of units sold (in hundreds). What is the maximum profit?

📌 The profit function is a quadratic \( P = -2x^2 + 12x - 5 \), which opens downward.

📌 The vertex occurs at \( x = -\frac{b}{2a} = -\frac{12}{2(-2)} = 3 \).

📌 Substitute \( x = 3 \):

📌 \( P = -2(3)^2 + 12(3) - 5 = -18 + 36 - 5 = 13 \).

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\(x = \pm 3\):
rac{9}{9} + rac{y^2}{4} = 1 \Rightarrow 1 + rac{y^2}{4} = 1 \Rightar...
Points: \((3, 0), (-3, 0)\)
Thus, the lattice points are: \((0, 2), (0, -2), (3, 0), (-3, 0)\).
Total number of lattice points: 4.
Question:** What is the base-ten number represented by the base-six nu...
To convert \(5432_6\) to base ten, use the digit-value expansion:
\cdot 6^3 + 4 \cdot 6^2 + 3 \cdot 6^1 + 2 \cdot 6^0
6^3 = 216 \Rightarrow 5 \cdot 216 = 1080
6^2 = 36 \Rightarrow 4 \cdot 36 = 144

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