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Home » Zerfallsformel**: \(Q = Q_0 \left(\frac12\right)^t/T\) - IX Labs

Zerfallsformel**: \(Q = Q_0 \left(\frac12\right)^t/T\) - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 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

📌 3x = 24 \quad \Rightarrow \quad x = 8

📌 Thus, the value of \(x\) that makes the vectors orthogonal is \(oxed{8}\).

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