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Probability first green: 6/15 - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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🔥 Popular Posts

egin{pmatrix} 0 & -1 \ 1 & 0 \end{pmatrix}
Scaling by 2 multiplies the entire transformation matrix by 2:
\mathbf{M} = 2 egin{pmatrix} 0 & -1 \ 1 & 0 \end{pmatrix} = egin{pma...
Thus, the required matrix is \(oxed{egin{pmatrix} 0 & -2 \ 2 & 0 \en...
A civil engineer analyzing directional stability in solar panel arrays...
Let \(\mathbf{v} = egin{pmatrix} x \ y \ z \end{pmatrix}\), \(\mathbf...
\mathbf{v} imes \mathbf{a} = egin{vmatrix}
\end{vmatrix} = \mathbf{i}(y \cdot 3 - z \cdot 2) - \mathbf{j}(x \cdot...
= egin{pmatrix} 3y - 2z \ - (3x - z) \ 2x - y \end{pmatrix} = egin{p...
Set equal to \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\):

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f(2) = 2 + rac{1}{2} = rac{5}{2}.
Equality holds when $ x = y $, which satisfies $ x, y > 0 $. Thus, the...
oxed{rac{5}{2}}.
Question: A hydrologist models the flow resistance $ R $ through a por...
R = rac{p + q}{p - q} + rac{p - q}{p + q} - 2,
where $ p > q > 0 $ are hydraulic conductivity parameters. Find the mi...
Solution: Let $ a = rac{p + q}{p - q} $ and $ b = rac{p - q}{p + q}...
R = a + rac{1}{a} - 2.
Define $ f(a) = a + rac{1}{a} - 2 $ for $ a > 1 $. By AM-GM, $ a + r...
R = rac{(p+q)^2 + (p-q)^2}{(p-q)(p+q)} - 2 = rac{p^2 + 2pq + q^2 + p...

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