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Home » A cube has a space diagonal of \(6\sqrt3\) cm. What is the volume of the cube? - Dyverse

A cube has a space diagonal of \(6\sqrt3\) cm. What is the volume of the cube? - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Compute the dot product:
\vec{v} \cdot \vec{w} = (2)(x) + (-1)(4) = 2x - 4
Set equal to zero:
2x - 4 = 0 \implies 2x = 4 \implies x = 2
Thus, when \( x = 2 \), the vectors are perpendicular, modeling balanc...
Question:** A science educator building a model of planetary motion us...
Let \( w = z^3 \). Then the equation becomes:
w^2 + w + 1 = 0
w = \frac{-1 \pm \sqrt{1^2 - 4(1)(1)}}{2} = \frac{-1 \pm \sqrt{-3}}{2}...
So \( z^3 = \omega \) or \( z^3 = \omega^2 \), where \( \omega = e^{2\...

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