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Home » The Ultimate Guide to He Mans Mastery of the Universe—You Won’t Want to Miss This! - Appcentric

The Ultimate Guide to He Mans Mastery of the Universe—You Won’t Want to Miss This! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Substitute \( p = 2 \) into (4):

📌 3(2) + q = 8 \implies 6 + q = 8 \implies q = 2

📌 Substitute \( p = 2 \), \( q = 2 \) into (1):

📌 + 2 + r = 10 \implies r = 6

📌 Thus, \( p = 2 \), \( q = 2 \), \( r = 6 \).

📌 \boxed{p = 2, \, q = 2, \, r = 6}

📌 \]Question: A tech entrepreneur in Athens designs a drone navigation system where the drone's path is represented by unit vectors $\mathbf{u}$ and $\mathbf{v}$ with an angle $\theta$ between them. If $\mathbf{u} \cdot \mathbf{v} = \frac{\sqrt{3}}{2}$, find $\theta$.

📌 Solution: The dot product of two unit vectors is $\mathbf{u} \cdot \mathbf{v} = \cos\theta$. Given $\cos\theta = \frac{\sqrt{3}}{2}$, the angle $\theta$ satisfies $\theta = \arccos\left(\frac{\sqrt{3}}{2}\right)$. This corresponds to $\theta = 30^\circ$ or $\frac{\pi}{6}$ radians. However, since cosine is positive in both the first and fourth quadrants, but angles between vectors are typically taken in $[0, \pi]$, the solution is $\boxed{\dfrac{\pi}{6}}$.

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Try including 2: then we need sum of distinct odd primes â¡ 37 mod 2...
So check: 39 = 2 + 37? Yes, 2 and 37 are distinct primes.
Is 37 â¤ 39 and prime? Yes.
And 2 + 37 = 39, and distinct â valid.
Check if 39 is the maximum possible. Can we get 39? Yes.
Is 40 possible? No, upper bound is less than 40.
Is 39 the maximum? Yes, since 38, 37, etc., are smaller.
But confirm: could 38 be written as sum of distinct primes?
is even. Use multiple odd primes.
Try largest primes < 38: 37 + 1 â 1 not prime.

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