In the packaging part of a warehouse, boxes of blue cups must be moved from the staging area located at an origination point along a conveyor belt described by a vector with components ⟨6, 30⟩. If boxes of red cups are moved 2.5 times the distance along the same belt, which describes the vector that shows the path of the boxes of red cups? Round the magnitude to the nearest whole number if necessary.
Answer
A
components: ⟨2.4, 12⟩, magnitude: about 31
B
components: ⟨2.4, 12⟩, magnitude: about 76
C
components: ⟨15, 75⟩, magnitude: about 31
D
components: ⟨15, 75⟩, magnitude: about 76
Explanation
Moving 2.5 times as far along the same belt multiplies each component by 2.5: ⟨6 × 2.5, 30 × 2.5⟩ = ⟨15, 75⟩. The magnitude is √(15² + 75²) = √5850 ≈ 76, so the correct choice is ⟨15, 75⟩ with magnitude about 76.
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