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Home » Donatello TMNT: The Secret Master Builder Revealed in Stunning Detail! - Abu Waleed Tea

Donatello TMNT: The Secret Master Builder Revealed in Stunning Detail! - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Only \( x = -1 + 2\sqrt{3} \approx 2.46 > 1 \) is valid (domain: \( x > 1 \))

📌 #### \( x = -1 + 2\sqrt{3} \)

📌 Find the sum of the infinite geometric series with first term 5 and common ratio \( \frac{2}{3} \).

📌 Sum \( S = \frac{a}{1 - r} = \frac{5}{1 - \frac{2}{3}} = \frac{5}{\frac{1}{3}} = 15 \)

📌 #### Sum: 15

📌 The angle between two vectors \( \vec{u} = \langle 3, 4 \rangle \) and \( \vec{v} = \langle -1, 2 \rangle \) is what in degrees?

📌 Use dot product: \( \vec{u} \cdot \vec{v} = 3(-1) + 4(2) = -3 + 8 = 5 \)

📌 Magnitudes: \( |\vec{u}| = \sqrt{9 + 16} = 5 \), \( |\vec{v}| = \sqrt{1 + 4} = \sqrt{5} \)

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