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how do you measure a tv - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Thus, the coordinates of the fourth vertex are:

📌 \boxed{(1, 1, 1)}

📌 Question:** An entomologist is analyzing the orthogonality of vectors representing insect flight paths. Find \(x\) such that the vectors \(\begin{pmatrix} 2 \\ 3 \\ x \end{pmatrix}\) and \(\begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix}\) are orthogonal.

📌 \begin{pmatrix} 2 \\ 3 \\ x \end{pmatrix} \cdot \begin{pmatrix} -1 \\ 4 \\ 2 \end{pmatrix} = 2(-1) + 3(4) + x(2)

📌 + 12 + 2x = 0

📌 Solving for \(x\):

📌 2x = -10 \quad \Rightarrow \quad x = -5

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P'(x) = -\frac{5000}{x^2} - 0.5
This is always negative, meaning \( P(x) \) is decreasing? But that ca...
Actually,
P(x) = \frac{5000}{x} + 120 - 0.5x
P'(x) = -\frac{5000}{x^2} - 0.5 \quad \text{— still negative?}
Wait — no, derivative of \( -0.5x \) is \( -0.5 \), derivative of \( 5...
This is always negative, meaning cost per unit decreases as \( x \) in...
Wait — cost per unit: \( P(x) = \frac{5000}{x} + 120 - 0.5x \)
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Likely a typo in interpretation. For realistic models, average cost ty...

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