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where to watch cleveland browns vs new england patriots - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Question: An archaeologist finds 9 artifacts, 4 of which are pottery, 3 are tools, and 2 are jewelry. If she randomly selects 3 artifacts to display in a museum, how many selections include at least one of each category?

📌 Total number of ways to choose 3 artifacts from 9:

📌 So we compute the number of such combinations:

📌 $$Question: A drone flies along the line given by the parametric equations $ x = 2t + 1, y = -3t + 4, z = t $, where $ t $ is time in seconds. At what point on this line is the drone closest to the control station located at $ (5, -1, 3) $?

📌 To find the point on the line closest to a fixed point, we minimize the square of the distance function between the drones position and the control station.

📌 Let the drones position be $ (x, y, z) = (2t + 1, -3t + 4, t) $, and the control station be $ (5, -1, 3) $.

📌 Try rational root theorem: test $ w = 1 $:

📌 This is allowed since unit vectors can be identical.

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