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Home » Number with at least one "11": let’s use recurrence: - 500apps

Number with at least one "11": let’s use recurrence: - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 an 120^\circ = an(180^\circ - 60^\circ) = - an 60^\circ

📌 We know $ an 60^\circ = \sqrt{3} $, so:

📌 an 120^\circ = -\sqrt{3}

📌 Final answer: $ oxed{-\sqrt{3}} $

📌 Question: In a triangle with side lengths 13, 14, and 15 units, find the length of the longest altitude.

📌 s = rac{13 + 14 + 15}{2} = 21

📌 Area $ A $ is:

📌 A = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6}

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3x + 4y = 0
We also know that the magnitude of \(\mathbf{v}\) is 5 units:
\sqrt{x^2 + y^2} = 5 \quad \Rightarrow \quad x^2 + y^2 = 25
From \(3x + 4y = 0\), we can express \(y\) in terms of \(x\):
y = -\frac{3}{4}x
Substitute \(y = -\frac{3}{4}x\) into \(x^2 + y^2 = 25\):

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