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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: 📰 Redeem Promo Code 5983794 📰 Plugging In The Values After 6 Hours 6173343 📰 Shocking Features Of The Yamaha Piano Forte That Everyone Is Whispering About 6214605 📰 5The Rockford Lady Cavaliers Are A Wnba Team Based In Rockford Illinois That Was Established In 2022 As An Expansion Franchise They Are Part Of The Northwest Division In The Western Conference Of The Wnba This Article Highlights Key Milestones And Moments From The Teams Early Years Focused On The Insert A Signature In Word Integration Theme Which Symbolizes Marking Their Official Entrance And Legacy With A Fresh Bold Header In Each Era 9310300 📰 Tory Lanez Release Date 7166316 📰 Apple Scratches 4016 📰 Youll Never Guess What Happened When This Tie Dye Shirt Took Over Your Closet 5203647 📰 South Of Midnight Review 8710272 📰 Dhakas Hidden Gem Why This Capital City Will Take Your Breath Away 2998986 📰 A 7 B 5 7 30 23 3516636 📰 This Small Tiny Tap Changed How I Cleandiscover The Hidden Secret 903009 📰 Unlock Free Money The Shocking Truth Behind The Backdoor Roth Ira Secrets You Need To Know 2973137 📰 Galway Hotel Galway 8633508 📰 This 200 Nike Vomero 5 Gold Shoe Is Changing Running Game Forever Dont Miss Out 4033970 📰 Download Wine Mac 1624025