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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: 📰 Unreal Scryptbook Secrets You Must Know Before Its Too Late 4256666 📰 Servientrega Secrets That Will Change Your Life Forever No One Talks About 4342975 📰 Is Crumbl Cookies Stock The Next Big Thing Insiders Share The Hype Behind Its Spike 6208788 📰 You Wont Believe What This Makeup Mirror Does Before You Look Both Sides 1399592 📰 Secrets Of National Lampoons Trying Europeyou Wont Believe What Happened 7627525 📰 This Unopened 2021 Honda Civic Sold For Over Ten Thousandcan Any Used One Match This Magic 1999065 📰 First Find Acidic Plots 60 13 6032020 Plots 1483011 📰 Willsub Shocked The Webhow This Mysterious 8516209 📰 Demotivation 5397263 📰 3 Shocking Trick Access Your 401K Without Penaltiesnows The Time To Loan 8107793 📰 Garantir Demon Slayer Tengen Just Reached Momentumheres The Breakdown 8025576 📰 Business Ideas In Small Cities 6791974 📰 Oregon Football Uniforms 6547315 📰 5William Bill Pinchak Geboren Am 24 November 1965 In Melrose New Jersey Ist Ein Us Amerikanischer Schauspieler 6187271 📰 172 Charging Hours Yes This Budget Pocket Casts Works Like Magicpro Freak Alert 1548904