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Home » The smallest such \( k \) is \( oxed263 \). - Moon Smoking

The smallest such \( k \) is \( oxed263 \). - Moon Smoking

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 A_{\text{new}} = \frac{\sqrt{3}}{4}(1.5s)^2 = \frac{\sqrt{3}}{4} \cdot 2.25s^2 = \frac{2.25\sqrt{3}}{4}s^2

📌 Ratio of New Area to Original Area:

📌 The ratio is:

📌 \text{Ratio} = \frac{A_{\text{new}}}{A_{\text{original}}} = \frac{\frac{2.25\sqrt{3}}{4}s^2}{\frac{\sqrt{3}}{4}s^2} = \frac{2.25\sqrt{3}/4}{\sqrt{3}/4} = 2.25

📌 Thus, the ratio of the new area to the original area is \(\boxed{2.25}\).**Question:

📌 An angel investor is evaluating the growth of a tech startup's user base, modeled by \( U(t) = t^2 + 3t + 5 \). At what time \( t \) will the user base reach 20,000 users? Solve for \( t \).

📌 To find the time \( t \) when \( U(t) = 20,000 \), set up the equation:

📌 \[ t^2 + 3t + 5 = 20,000 \]

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