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Home » Now, the sequence of 3-digit multiples of 7 is: - Anadea

Now, the sequence of 3-digit multiples of 7 is: - Anadea

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 The lowest point is at $x = 0$: $y = 5$.

📌 Vertical distance = $13 - 5 = 8$ meters.

📌 A software engineer implements a 3D rotation using quaternions. The rotation of $90^\circ$ about the $y$-axis is represented by the quaternion $q = \cos( heta/2) + \sin( heta/2)i$, where $ heta = 90^\circ = rac{\pi}{2}$. What is the scalar part of $q$?

📌 $ heta/2 = \pi/4$, so $\cos(\pi/4) = rac{\sqrt{2}}{2}$, $\sin(\pi/4) = rac{\sqrt{2}}{2}$.

📌 The scalar (real) part of $q$ is $\cos(\pi/4) = rac{\sqrt{2}}{2}$.

📌 #### $rac{\sqrt{2}}{2}$

📌 A micropaleontologist uses carbon-14 dating on a foraminifera sample. If the sample has 35% of its original carbon-14 remaining, and the half-life of carbon-14 is 5730 years, how old is the sample? Use $N = N_0 e^{-kt}$, $k = rac{\ln 2}{5730}$.

📌 Given $N/N_0 = 0.35 = e^{-kt}$, so $\ln(0.35) = -kt$.

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