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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: 📰 Texas Tech Vs Wvu Football 9842957 📰 1V1 Online Games The Shocking Secrets Exposed That Will Blow Your Mind 9662350 📰 Aquaman Cast 5409724 📰 How To Set Default Font In Outlook 9326690 📰 Java Se 7U80 Secrets Revealed Transform Your Development With This Kit 4439623 📰 Barcelona Falls Flat Dortmund Shocks The Shocking Stats That Changed Everything 9913620 📰 Cranberry Bog Spiders Exposed The Creepy Creatures Invading Your Backyard You Wont Believe Their Size 7811733 📰 Jlo And Kevin Costner 8473395 📰 You Wont Believe What Happened When Caterpillar Stock Dividedmarket Explodes Boom Alert 9819253 📰 Chicken Diapers 253466 📰 5S Learn The Operator Program In Java Your Gateway To Cleaner Powerful Code Forever 3495692 📰 Alternatively Using Formula For Perpendicular Component Magnitude 7281206 📰 This Quartists Haunting Performance Revealed The Power Of Silent Sound 9480257 📰 Npc Revealedheres What Most People Dont Know About Non Playable Characters 5204505 📰 Jennifer Lawrenc Enude 5027352