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Home » 因此，$ b_3 = -2.625 = -\frac218 $ - RTA

因此，$ b_3 = -2.625 = -\frac218 $ - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 A VR developer encodes spatial coordinates into cubic units. A virtual room is modeled as a cube with side length equal to the smallest integer greater than \( \sqrt{200} \). What is the volume of the room in cubic units?

📌 \( \sqrt{200} \approx 14.142 \), so side length = 15. Volume = \(15^3 = 3375\).

📌 An angel investor evaluates a biotech firm whose projected revenue follows the quadratic model \( R(x) = -2x^2 + 40x + 100 \), where \( x \) is years after launch. In which year does revenue peak?

📌 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: \( \frac{4}{3}\pi r^3 = 216 \) → \( r^3 = \frac{162}{\pi} \approx 51.57 \) → \( r \approx 3.72 \).

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