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Home » -3t^2 + 18t - 24 = 0 - Simpleprint

-3t^2 + 18t - 24 = 0 - Simpleprint

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 An anthropologist is studying the cultural significance of ancient structures that align with celestial bodies. They model the direction vector of a sunrise alignment as \(egin{pmatrix} 3 \ 4 \end{pmatrix}\) and need to find a perpendicular direction vector for a shadow alignment. Find \(x\) so that the vectors \(egin{pmatrix} 3 \ 4 \end{pmatrix}\) and \(egin{pmatrix} x \ -6 \end{pmatrix}\) are orthogonal.

📌 Two vectors \(egin{pmatrix} a \ b \end{pmatrix}\) and \(egin{pmatrix} c \ d \end{pmatrix}\) are orthogonal if their dot product is zero: \(a \cdot c + b \cdot d = 0\).

📌 Given vectors:

📌 egin{pmatrix} 3 \ 4 \end{pmatrix} \quad ext{and} \quad egin{pmatrix} x \ -6 \end{pmatrix}

📌 3x + 4(-6) = 0

📌 3x - 24 = 0

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