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📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 Solution: Let the original side length of an equilateral triangle be $ s $. The area $ A $ of an equilateral triangle is given by:

📌 We are told this area is $ 27 $, so:

📌 Now, if the side length doubles, the new side is $ 2s $, and the new area becomes:

📌 Question: A neuroscientist models neural signal cycles as periodic functions and observes that one pattern repeats every $ 48 $ milliseconds and another every $ 72 $ milliseconds. After how many milliseconds will both signals align precisely at the same time again?

📌 Solution: We are to find the least common multiple (LCM) of $ 48 $ and $ 72 $. First, factor both numbers:

📌 Question: A geologist uses satellite imaging to study a square geothermal field. To analyze coverage efficiently, she divides the region into non-overlapping rectangles of size $ 2 imes 3 $ kilometers. What is the smallest number of such rectangles needed to exactly cover a square region of side length $ 6 $ kilometers?

📌 Now, $ k $ is a positive multiple of $ 6 $, so possible values less than $ 12 $ are $ 6 $ and $ 12 $. But $ k < 12 $, so $ k = 12 $ is excluded.

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