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📰 Question: A mammalogist observes that the social cohesion index $ S $ of a primate group over time is modeled by $ S = \left| \sin\left(\frac{3\pi}{7} t\right) + \cos\left(\frac{4\pi}{7} t\right) \right| $, where $ t $ is time in days. How many times in one full cycle of $ S $ (i.e., over $ t \in [0, 7) $) does $ S = 1 $? 📰 Solution: The function $ S(t) = \left| \sin\left(\frac{3\pi}{7} t\right) + \cos\left(\frac{4\pi}{7} t\right) \right| $ has period $ T $, where both components repeat. The fundamental period is the least common multiple of the periods of $ \sin\left(\frac{3\pi}{7} t\right) $ and $ \cos\left(\frac{4\pi}{7} t\right) $. 📰 The angular frequencies are $ \frac{3\pi}{7} $ and $ \frac{4\pi}{7} $, so periods are $ \frac{2\pi}{3\pi/7} = \frac{14}{3} $, and $ \frac{2\pi}{4\pi/7} = \frac{7}{2} $. The LCM of $ \frac{14}{3} $ and $ \frac{7}{2} $ is found by expressing as rational multiples. 📰 Discover The Lamborghini Huracan On The Marketunbelievable Price From A Dream Ride 3968455 📰 Ken And Barbie Killers 4588651 📰 6Question An Ancient Andean Ceremonial Platform Is Shaped Like A Regular Hexagon With Side Length 5 Meters If Each Side Is Extended Outward By 2 Meters To Form A Larger Regular Hexagon By How Many Square Meters Does The Area Increase 6444904 📰 Vitueal Oz Sumer Wars 2639500 📰 Sushi Co Broadway 7456275 📰 You Wont Believe How Anti Kickback Laws Cannot Shock Youheres Everything You Must Know 5193987 📰 Bath And Body Jobs 3384716 📰 Ford Headquarters Move 2866706 📰 2 Dollar Robux Gift Card 2344208 📰 Ctr845 Pro Gt Autoclicker Revealed The Ultimate Trick To Supercharge Your Sales Tonight 2789186 📰 Sichuan Garden 4233199 📰 The Ultimate Breakdown Cast Of Angry Birds Movie 3 Thats Taking The Internet By Storm 1610441 📰 She Said It Best Sydney Sweeneys Pussy Moment Drove Fans Madand Drove Traffic 9754534 📰 From Oversized To Slimsee What 195 Pounds Equal In Kilograms Fast 8490595 📰 Vacation Dress 6496992