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Home » But inequality: \( t > 20 \), so smallest integer t is 21. - ToelettAPP

But inequality: \( t > 20 \), so smallest integer t is 21. - ToelettAPP

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 An anthropologist is studying the cultural significance of ancient structures that align with celestial bodies. They model the direction vector of a sunrise alignment as \(egin{pmatrix} 3 \ 4 \end{pmatrix}\) and need to find a perpendicular direction vector for a shadow alignment. Find \(x\) so that the vectors \(egin{pmatrix} 3 \ 4 \end{pmatrix}\) and \(egin{pmatrix} x \ -6 \end{pmatrix}\) are orthogonal.

📌 Two vectors \(egin{pmatrix} a \ b \end{pmatrix}\) and \(egin{pmatrix} c \ d \end{pmatrix}\) are orthogonal if their dot product is zero: \(a \cdot c + b \cdot d = 0\).

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#### 6x + 5
If a train travels at 60 km/h for 2.5 hours, how far does it travel?
Distance is given by \( speed \times time \).
Calculating, \( 60 \, \text{km/h} \times 2.5 \, \text{hours} = 150 \,...
Evaluate the integral \( \int (2x + 3) \, dx \).
The integral of \( 2x \) is \( x^2 \) and the integral of \( 3 \) is \...
Thus, \( \int (2x + 3) \, dx = x^2 + 3x + C \), where \( C \) is the c...
#### x^2 + 3x + C**1.
A car travels 150 miles at a speed of 50 mph and then another 100 mile...
First, calculate the total distance: \(150 + 100 = 250\) miles.

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