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Home » Big Macintoshcheck: The Giant Mac That’s Taking Tech by Storm! - inBeat

Big Macintoshcheck: The Giant Mac That’s Taking Tech by Storm! - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 and between $(1,1,0)$ and $(1,0,1)$: $\sqrt{(0)^2 + (-1)^2 + (1)^2} = \sqrt{2}$, etc. All edges $\sqrt{2}$. Thus, the fourth vertex is $(0,1,1)$.

📌 \boxed{(0, 1, 1)}

📌 Question: Find all angles $z \in [0^\circ, 360^\circ]$ satisfying $2\sin^2 z - 3\sin z + 1 = 0$.

📌 Solution: Let $u = \sin z$. The equation becomes $2u^2 - 3u + 1 = 0$. Solving:

📌 u = \frac{3 \pm \sqrt{9 - 8}}{4} = \frac{3 \pm 1}{4} \implies u = 1 \text{ or } u = \frac{1}{2}.

📌 For $\sin z = 1$: $z = 90^\circ$.

📌 For $\sin z = \frac{1}{2}$: $z = 30^\circ, 150^\circ$.

📌 Thus, solutions are $30^\circ, 90^\circ, 150^\circ$.

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