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Home » Thus, the sum becomes a telescoping series: - Londonproperty

Thus, the sum becomes a telescoping series: - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Thus, the minimum value is 2.

📌 A cube has a surface area of 6 square meters. What is the volume of the cube in cubic meters?

📌 Let \( s \) be the side length. Surface area = \( 6s^2 = 6 \).

📌 So, \( s^2 = 1 \), and \( s = 1 \).

📌 Volume = \( s^3 = 1 \).

📌 Find the number of integer solutions to the inequality \( |2x - 5| \leq 7 \).

📌 This inequality becomes \( -7 \leq 2x - 5 \leq 7 \).

📌 Add 5: \( -2 \leq 2x \leq 12 \).

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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 \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\):
3y - 2z = 0 \
-3x + z = 0 \
2x - y = 5
From second equation: \(z = 3x\)
From first: \(3y = 2z = 2(3x) = 6x \Rightarrow y = 2x\)

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