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Home » Is Xbox Prime the Hidden Game Pass for Ultimate Xbox Loyalty? - Leaselab

Is Xbox Prime the Hidden Game Pass for Ultimate Xbox Loyalty? - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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\mathbf{c} \cdot \mathbf{c} = 1^2 + 2^2 + (-1)^2 = 1 + 4 + 1 = 6
ext{proj}_{\mathbf{c}} \mathbf{v} = rac{-3}{6} egin{pmatrix} 1 \ 2 \...
Now compute the perpendicular component:
\mathbf{v}_{\perp} = egin{pmatrix} 2 \ -1 \ 3 \end{pmatrix} - egin{p...
The magnitude of the perpendicular component (which is the desired qua...
\|\mathbf{v}_{\perp}\| = \sqrt{(2.5)^2 + 0^2 + (2.5)^2} = \sqrt{6.25 +...
Alternatively, using formula for perpendicular component magnitude:
\|\mathbf{v}_{\perp}\| = \sqrt{\|\mathbf{v}\|^2 - \left(rac{|\mathbf{...
But since we already computed it:
oxed{\dfrac{5\sqrt{2}}{2}}

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\frac{z_A + z_B + z_C}{3} = 12
Let $ z_A = a, z_B = b, z_C = c $. Then:
\frac{a + b + c}{3} = 12 \Rightarrow a + b + c = 36
Now, the elevation at the centroid is a weighted average of the height...
\frac{a + b + c}{3} = 12
Thus, the $ z $-coordinate of the centroid is consistent with the aver...
\boxed{\frac{11}{3}}
Question: An anthropologist is modeling cultural diffusion between thr...
Solution: First, compute the center of mass (centroid) of triangle $ A...
G = \left( \frac{0 + 6 + 3}{3}, \frac{0 + 0 + 6}{3} \right) = (3, 2)

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