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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: 📰 Temps Pour Remplir La Moiti Du Rservoir 20 Minutes 📰 Temps Pour Remplir Le Rservoir Entier Frac200 Text Litres5 Text Litresminute 40 Text Minutes 📰 Temps Pris De La Ville A La Ville B Fracd60 Heures 📰 Temps Pris De La Ville B La Ville A Fracd40 Heures 📰 Temps Total Pour Le Trajet Aller Retour Fracd60 Fracd40 📰 Termed The Ultimate Thrill Anaconda The Hunt Blood Orchids Bloody Legacy Revealed 📰 Terrifying Legacy Top 5 Texas Chainsaw Movies That Will Give You Chills 📰 Texttime Frac90Pi2 Approx 14137 Text Minutes 📰 Texttime Approx 141 Text Minutes 📰 That 2014 Ninja Turtles Movie Is A Hidden Masterpieceyou Need To See It 📰 The 1 Flex Of Mr Natural How He Achieves Brotherhood Progress In Moments 📰 The 1 Guide To Mtg Rules Every Player Needs Before Game Day 📰 The 1 Minecraft Map Seed That Changed How Players Explore The Blocky Universe 📰 The 1 Mlg Review Thats Dominating Online Chats Right Now 📰 The 1 Most Played Games Right Now Never Miss These Top Hits