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📰 \]Question: A weather balloon is modeled as a sphere with radius $ r $ meters, and it ascends such that its volume increases at a rate proportional to $ \sin \theta $, where $ \theta $ is the angle of elevation from the ground. If the volume increase rate is given by $ \frac{dV}{dt} = k \sin \theta $, and $ \theta = 60^\circ $, compute the rate of volume increase in terms of $ k $ and $ r $. 📰 Solution: The volume of a sphere is given by $ V = \frac{4}{3} \pi r^3 $. Differentiating with respect to time $ t $, we get: 📰 We are given that $ \frac{dV}{dt} = k \sin \theta $, and $ \theta = 60^\circ $, so $ \sin \theta = \frac{\sqrt{3}}{2} $. Substituting: 📰 Citrus New Windsor Ny 6287436 📰 18 425 Not 5714477 📰 Sorprende A Los Nostros Favoritos Feliz Cumpleaos En Espaol Con Estas Frases 8502240 📰 Act Of Contrition Thats Going Viralsee Why Millions Are Talking About Forgiveness Today 3752002 📰 This Revolutionary Saw Blowing Hack Blows Everyone Awayshocking Reveal 8671607 📰 Online Soccer Games That Are Revolutionizing How You Playheres How 4945929 📰 The Ultimate Guide To Chair Conformation Its Time To Rewire Your Sitting Habits 5183775 📰 Dr Taylor 7608042 📰 The Legendary Big Chief Holds Power That Will Shock You 940009 📰 Aprilaire Snaps Why This Seasons Early Warmth Is Actually Changing Your Life Forever 9687561 📰 Chogath Build 1250167 📰 Regal Metropolitan Stadium Where Sports And Splendor Collide Like Never Before 3957274 📰 Discover Short I Words That Will Make You Sound Smarterin Seconds 2598398 📰 Wells Fargo Checking Sign In 1814952 📰 Yahoo Microstrategy 534217