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Home » Volume formula: \( V = rac13 \pi r^2 h \) - AMAZONAWS

Volume formula: \( V = rac13 \pi r^2 h \) - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Question:** An entomologist is analyzing the orthogonality of vectors representing insect flight paths. Find \(x\) such that the vectors \(\begin{pmatrix} 2 \\ 3 \\ x \end{pmatrix}\) and \(\begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix}\) are orthogonal.

📌 \begin{pmatrix} 2 \\ 3 \\ x \end{pmatrix} \cdot \begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix} = 2(-1) + 3(4) + x(2)

📌 + 12 + 2x = 0

📌 Solving for \(x\):

📌 2x = -10 \quad \Rightarrow \quad x = -5

📌 \boxed{-5}

📌 Question:** A biodiversity specialist is studying the periodic behavior of genetic expression modeled by the equation \(2\cos(2z) = \sqrt{3}\). Find the sum of all angles \(z \in [0^\circ, 360^\circ]\) that satisfy this equation.

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