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Home » where $ r = 2x $ and $ l = 5x $. Substituting: - Londonproperty

where $ r = 2x $ and $ l = 5x $. Substituting: - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Using the trigonometric identity \( \sin(2\theta) = 2\sin\theta\cos\theta \), we rewrite the expression as

📌 \[ x = \frac{v_0^2 \sin(2\theta)}{2g}. \]

📌 Therefore, the horizontal distance is

📌 \[\boxed{\frac{v_0^2 \sin(2\theta)}{2g}}.\]

📌 A deep-sea extremophile genomics researcher is studying the growth dynamics of microbial communities near hydrothermal vents. The population of a certain microbial species is modeled by the equation \( P(t) = P_0 e^{kt} \), where \( k \) is a growth constant. If the population triples in 5 hours, what is the value of \( k \)?

📌 We are given the population model

📌 \[ P(t) = P_0 e^{kt}, \]

📌 and that the population triples in 5 hours, so

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