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Home » 4x² + 42x - 72 = 0 - AIKO, infinite ways to autonomy.

4x² + 42x - 72 = 0 - AIKO, infinite ways to autonomy.

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 $ a_6 = 13 + 8 = 21 $

📌 So 21 sequences with no two consecutive 3s.

📌 Total sequences: $ 2^6 = 64 $

📌 Thus, number with **at least one** "33" is $ 64 - 21 = 43 $

📌 Therefore, the answer is $ \boxed{43} $.

📌 \boxed{43}**Question: A vector \(\mathbf{v}\) satisfies \(\mathbf{v} \times \mathbf{b} = \begin{pmatrix} 0 \\ 3 \\ -4 \end{pmatrix}\) for \(\mathbf{b} = \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix}\). Find \(\mathbf{v}\).

📌 Given \(\mathbf{v} \times \mathbf{b} = \begin{pmatrix} 0 \\ 3 \\ -4 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix}\), let \(\mathbf{v} = \begin{pmatrix} v_1 \\ v_2 \\ v_3 \end{pmatrix}\).

📌 The cross product \(\mathbf{v} \times \mathbf{b}\) is:

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