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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. 📰 Roasted Almonds 1058243 📰 From Humble Beginnings To Stardombernice Juliens Life Secrets You Need To Know 9746556 📰 The Surprising Truth Behind These 7 Little Words The 7 Little Words 7 Phenomenon 6306191 📰 Vertex Stock Soared Over 200Learn The Hidden Strategy Thats Changing Investor Minds 2748608 📰 Total Time Total Distance Speed 780 45 780451733317333 Hours 7080638 📰 Scrolls 1076842 📰 Pfizer Inc Surpasses 100 Billion Market Capyahoo Finance Reveals Shocking Surge 1248516 📰 Chaffle Recipes Youve Never Tried Estas Delicious Surprises Will Win Your Heart 3458030 📰 The Ultimate Guide To Super Metroids Hidden Treasures Youre Going Crazy 1281769 📰 Chicago Cubs Unravel Distance Record In Shocking Final Gamewhat Happened 8668447 📰 Only 1 Donatediscover Why 99 Of Patients Depend On Regular Blood Donations 9450300 📰 Wait A Minutethis White Graduation Dress Is Turning Heads Like No Other You Wont Believe How Stunning She Looks In This Timeless Elegant Gown Every Fold Every Detail Sums Up Pure Grace In White Dont Miss The Secret That Makes This Dress Unforgettable At Any Ceremony 2159235 📰 187Ml To Oz 3291918 📰 Hhs Fund Revealed How This 500 Million Could Transform Public Health Programs Today 9535552 📰 Doom Dark Ages Revealed The Darkest Moments Gamers Never Want To Remember 8040521