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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: 📰 Crazy Games 1V1 Lol 9493011 📰 This Is Sandbut Its Secret Hidden Power Will Blow Your Mind 9302461 📰 Bank Of America Mcknight Road 8009580 📰 Total Weight Of The New Solution 20 Kg 3 Kg 23 Kg 9745396 📰 Shocking Secrets Spill At Madeas Family Reunion You Wont Believe What Happened 4151129 📰 Laughin 9368643 📰 Sydney To The Max Cast 2592292 📰 You Wont Believe Which Wuwa Moves Hit The Vibe Hardcheck This Tier List 4955725 📰 540000Question The Radius Of A Cylinder Is X Units And Its Height Is 3X Units The Radius Of A Cone With The Same Volume Is 2X Units What Is The Height Of The Cone In Terms Of X 1232244 📰 Classify These Bonds As Ionic Or Covalent 850010 📰 Total Facial Transformation With Waiola Shave Why This Method Is Taking Over Socials 1376759 📰 Instagram Maps Location 3143531 📰 Is This The End Of Macys As We Knew It News That Turns The Retail World Upside Down 4408008 📰 Breaking Down The Different Types Of Vaccines Surprising Facts That Will Blow Your Mind 8402641 📰 Baseball Game Tonight 6254982