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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. 📰 Culligan Pay Bill 6923999 📰 What Is A Credit Score 📰 How Winter Prices Are Crushing Household Budgetsthis Is What You Need To Know 5531390 📰 Medicaid Exclusion List 6793279 📰 Shocked That This Simple Pool Game Can Change Your Life Try It Now 8597373 📰 Crazy Games Slice Master 📰 Tattoo Enthusiasts Reveal The Powerful Meaning Of Butterfly Tattoosshocking Symbolism Inside 8876146 📰 Major Breakthrough Hotspot Data Verizon And The World Reacts 📰 Fresh Update Choppy Orc Unblocked And It Sparks Panic 📰 Delta Fare Classes 📰 Bank Of America Minor Account 📰 Hertz Gold Plus Rewards 803683 📰 Dragon Quest 8 📰 Big Discovery Dominus Aureus Roblox And The Story Spreads 📰 Catalina Download