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Home » I Tried Protein Donuts – The Sweet Treat That’s Also a Powerhouse Mega Source of Protein! - Aurero

I Tried Protein Donuts – The Sweet Treat That’s Also a Powerhouse Mega Source of Protein! - Aurero

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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📌 Solve the quadratic:

📌 x = \frac{3 \pm \sqrt{9 - 8}}{4} = \frac{3 \pm 1}{4} \Rightarrow x = 1, \frac{1}{2}

📌 Now solve for $z$:

📌 $\sin z = 1 \Rightarrow z = 90^\circ$

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

📌 Thus, the solutions are:

📌 \boxed{30^\circ, 90^\circ, 150^\circ}

📌 Question: Find the value of $x$ so that the vectors $\begin{pmatrix} 2 \\ x \\ 3 \end{pmatrix}$ and $\begin{pmatrix} x \\ -1 \\ 4 \end{pmatrix}$ are orthogonal.

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