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hyatt vacation club at hacienda del mar - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Vertex of parabola: \( x = -\frac{b}{2a} = -\frac{40}{2 \cdot (-2)} = \frac{40}{4} = 10 \).

📌 A game designer uses trigonometric scaling to morph a cube into a sphere. If the cube’s edge length is 6 units, by what factor must the surface area be scaled to match the sphere’s surface area?

📌 Cube surface area: \(6 \cdot 6^2 = 6 \cdot 36 = 216\).

📌 Cube volume: \(6^3 = 216\), so sphere radius \( r \) from volume: \( \frac{4}{3}\pi r^3 = 216 \) → \( r^3 = \frac{162}{\pi} \approx 51.57 \) → \( r \approx 3.72 \).

📌 Sphere surface area: \(4\pi r^2 \approx 4\pi (13.83) \approx 173.6\).

📌 Scale factor: \( \frac{173.6}{216} \approx 0.803 \).

📌 #### 0.803

📌 A developer implements a fade-out effect where brightness decreases by 10% each second. If initial brightness is 800 lux, what is the brightness after 7 seconds?

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