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Home » Back Hyperextension: Why This Hidden Move Could Fix Your Chronic Back Pain! - Abbey Badges

Back Hyperextension: Why This Hidden Move Could Fix Your Chronic Back Pain! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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., \( y = 0 \).

📌 Thus, the maximum value of \( f(x, y) \) is:

📌 This maximum is attainable within the field, for example at \( (x, y) = \left(\frac{r}{2}, 0\right) \).

📌 Therefore, the maximum nutrient concentration is:

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