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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. 📰 Gale Hotel South Beach Miami Fl 4102668 📰 How To Claim Your Mission Lane Credit Card Access Its Easier Than You Think 110486 📰 Why This Phrase Has Everyone Obsessed And Medical 5082074 📰 The Mysterious Upgrade Everyones Racing In Secrets Bobber Motorcycle Unleashed 4921249 📰 Touch Vpn Unlocked The Secret Method That No One Talks About 6791571 📰 You Wont Believe How Azure Disk Storage Pricing Shakes Up Cloud Costs In 2024 9564325 📰 You Wont Believe What Happens When You Log Into Kantime 704107 📰 High Society 1956 3550829 📰 Cast Of School Spirits 6422972 📰 This Simple Sauce Turneo Your Taste Buches Like Never Before 7589505 📰 Diaper Size Chart 7758293 📰 The Shocking Ingredient Making Sugar Free Chocolate Addicting And Nutritious 5022046 📰 Vzw Switch Plan 801847 📰 Bankofamericasign 2266914 📰 Chart Bitcoin 183964