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sql cast as int - All Square Golf

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 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:

📌 Question:** An electrical engineer analyzes the magnetic flux through a coil whose area vector \( \vec{A} \) rotates in the \( xy \)-plane. If \( \vec{A}(t) = A_0 \cos(\omega t) \hat{\mathbf{x}} + A_0 \sin(\omega t) \hat{\mathbf{y}} \) and the magnetic field is \( \vec{B} = B_0 \hat{\mathbf{z}} \), compute the time average of the magnetic flux \( \Phi_B = \vec{B} \cdot \vec{A}(t) \) over one period.

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