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Home » The Ultimate Countdown: Xbox One Release Schedule Revealed! Are You Ready? - Blask

The Ultimate Countdown: Xbox One Release Schedule Revealed! Are You Ready? - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Solution: To determine the smallest positive angle at which the robot returns to its original orientation, we must find the least common multiple (LCM) of the two rotation increments, $12^\circ$ and $18^\circ$. First, factor both numbers:

📌 = 2^2 \cdot 3, \quad 18 = 2 \cdot 3^2

📌 The LCM is obtained by taking the highest powers of all prime factors:

📌 \text{LCM}(12, 18) = 2^2 \cdot 3^2 = 4 \cdot 9 = 36

📌 Thus, the smallest positive angle that returns the robot to its starting orientation is $ \boxed{36^\circ} $.

📌 Question: A geographer is analyzing population clusters using a grid where each cell represents a 1 km² area. If a city covers a region that is a perfect square of area $2025$ km², how many different square grid sizes (with integer side lengths) can evenly divide the area?

📌 Solution: The area of the city is $2025$ km², and we are to find how many integer side lengths $s$ correspond to square grid sizes such that $s^2$ divides $2025$. This requires finding the number of positive divisors of $2025$, since each such divisor $s^2$ implies $s$ is an integer divisor of $\sqrt{2025} = 45$.

📌 First, factor $2025$:

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