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Home » Multiplying both sides by $ x $: - DNSFLEX

Multiplying both sides by $ x $: - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Since there are 5 participants, each moving from a vertex to the center, the total distance traveled is:

📌 \times R = 5 \times 0.8507s = 4.2535s

📌 Thus, the total distance traveled by all participants is:

📌 \boxed{4.2535s}

📌 Question:** A soil scientist models the nutrient distribution in a circular field of radius \( r \) using the function \( f(x, y) = \sin\left(\frac{\pi x}{r}\right) + \cos\left(\frac{\pi y}{r}\right) \). Determine the maximum nutrient concentration within the field.

📌 The nutrient concentration is given by \( f(x, y) = \sin\left(\frac{\pi x}{r}\right) + \cos\left(\frac{\pi y}{r}\right) \). To find the maximum value, note that both sine and cosine functions achieve their maximum value of 1.

📌 The maximum of \( \sin\left(\frac{\pi x}{r}\right) \) is 1, occurring when \( \frac{\pi x}{r} = \frac{\pi}{2} + 2k\pi \), e.g., \( x = \frac{r}{2} \).

📌 The maximum of \( \cos\left(\frac{\pi y}{r}\right) \) is 1, occurring when \( \frac{\pi y}{r} = 2m\pi \), e.g., \( y = 0 \).

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