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Home » Get Irresistibly Spicy with Boom Boom Sauce – The Ultimate Flavor Bomb! - inBeat

Get Irresistibly Spicy with Boom Boom Sauce – The Ultimate Flavor Bomb! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 If $ n = \frac{3}{4} $, $ m = -\frac{16}{9} \cdot \frac{3}{4} = -\frac{4}{3} $. If $ n = -\frac{3}{4} $, $ m = \frac{4}{3} $.

📌 Check $ \vec{OG} \cdot (\vec{OA} + \vec{OB}) = 0 $: Both cases satisfy. However, the problem likely expects positive $ n $ (growth direction). Thus $ (m, n) = \left(-\frac{4}{3}, \frac{3}{4}\right) $.

📌 \boxed{\left( -\dfrac{4}{3}, \dfrac{3}{4} \right)}

📌 Question: The maximum imaginary part of a root of $ z^5 + z^3 + z + 1 = 0 $ can be expressed as $ \sin \theta $. Find $ \theta $ in degrees.

📌 Solution: Factor the polynomial:

📌 z^5 + z^3 + z + 1 = z^3(z^2 + 1) + 1(z + 1).

📌 Group terms:

📌 Roots: $ z^3 = -1 \implies z = e^{i\pi/3 + 2k\pi/3} $, and $ z^2 = -1 \implies z = e^{i\pi/2}, e^{i3\pi/2} $.

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