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Home » Los Angeles Nightmares: The Shocking True Crime Azootstrap of LA’s Forgotten Alleys - Leaselab

Los Angeles Nightmares: The Shocking True Crime Azootstrap of LA’s Forgotten Alleys - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Take derivative and set to 0:

📌 \frac{d}{dt}(6t^2 + 4t + 30) = 12t + 4 = 0 \Rightarrow t = -\frac{1}{3}

📌 Substitute $t = -\frac{1}{3}$ into $\vec{r}(t)$:

📌 \vec{r}\left(-\frac{1}{3}\right) = \begin{pmatrix} 1 + 2(-\frac{1}{3}) \\ -\frac{1}{3} \\ -3 - (-\frac{1}{3}) \end{pmatrix} = \begin{pmatrix} 1 - \frac{2}{3} \\ -\frac{1}{3} \\ -3 + \frac{1}{3} \end{pmatrix} = \begin{pmatrix} \frac{1}{3} \\ -\frac{1}{3} \\ -\frac{8}{3} \end{pmatrix}

📌 Thus, the closest point is:

📌 \boxed{\begin{pmatrix} \frac{1}{3} \\ -\frac{1}{3} \\ -\frac{8}{3} \end{pmatrix}}

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

📌 Two vectors are orthogonal if their dot product is zero. Compute the dot product:

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V_{ ext{receptor}} = rac{1}{2} \cdot rac{4}{3}\pi (3x)^3 = rac{2}{3...
Now compute the ratio:
rac{V_{ ext{particle}}}{V_{ ext{receptor}}} = rac{rac{4}{3}\pi x^3}{...
Final answer: $ oxed{rac{2}{27}} $
Question: Compute $ an 120^\circ $ using the unit circle and trigonom...
Solution: The angle $ 120^\circ $ lies in the second quadrant. Using t...
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}} $

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