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v^2 < 200 - Ready Digital AB

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Alternatively, perhaps the student meant a vector in the plane â but the cross product condition cannot be satisfied.

📌 After careful analysis, since the given vector \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\) is not orthogonal to \(egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\), no such \(\mathbf{v}\) exists.

📌 But to provide a constructive answer as intended, suppose we **require** the solution to minimize discrepancy. However, in olympiad style, we assert:

📌 There is no vector \(\mathbf{v}\) satisfying the equation because \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\) is not orthogonal to \(egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\), violating a fundamental property of the cross product.

📌 However, if we assume a typo and the result should be \(egin{pmatrix} 0 \ 0 \ k \end{pmatrix}\) with \(k = egin{pmatrix} 0 \ 0 \ \mathbf{a} \cdot \mathbf{u} \end{pmatrix}\), but none matches.

📌 Given the inconsistency, and to align with expected answer format, perhaps the problem meant:

📌 Find \(\mathbf{v}\) such that \(\mathbf{v} imes egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} = egin{pmatrix} -6 \ 3 \ 0 \end{pmatrix}\)? But we must work with given.

📌 Final conclusion: **No solution exists**, but since olympiads expect answers, likely a misinterpretation. Recheck:

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Expand left: \( 2a + dn - d = dn + (2a - d) \)
So: \( dn + (2a - d) = 6n + 10 \)
\( d = 6 \)
\( 2a - d = 10 \Rightarrow 2a - 6 = 10 \Rightarrow 2a = 16 \Rightarrow...
So common difference is 6.
A triangle has sides of length 7 cm, 24 cm, and 25 cm. What is the are...
Check if right triangle: \( 7^2 + 24^2 = 49 + 576 = 625 = 25^2 \) â...
So area = \( rac{1}{2} imes ext{leg1} imes ext{leg2} = rac{1}{2}...
The function \( f(x) = rac{2x + 1}{x - 3} \) has a horizontal asympto...
As \( x o \infty \), \( f(x) pprox rac{2x}{x} = 2 \)

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