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Home » $\boxed{\dfrac10x - 43}$ - Midis

$\boxed{\dfrac10x - 43}$ - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 The sum of three consecutive even integers is 102. What is the largest integer?

📌 Let the integers be \(x\), \(x+2\), \(x+4\).

📌 x + (x+2) + (x+4) = 102 \quad \Rightarrow \quad 3x + 6 = 102 \quad \Rightarrow \quad 3x = 96 \quad \Rightarrow \quad x = 32

📌 Largest integer: \(32 + 4 = 36\)

📌 #### 36Question: A startup is developing a medical device that uses vector-based sensor arrays to detect physiological signals. Suppose two sensor vectors are given as $\vec{v} = \begin{pmatrix} 3 \\ -2 \\ x \end{pmatrix}$ and $\vec{w} = \begin{pmatrix} x \\ 4 \\ -1 \end{pmatrix}$. Find the value of $x$ such that the vectors are orthogonal.

📌 Solution: For two vectors to be orthogonal, their dot product must be zero. Compute the dot product:

📌 \vec{v} \cdot \vec{w} = 3x + (-2)(4) + x(-1) = 3x - 8 - x = 2x - 8

📌 Set the dot product equal to zero:

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