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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: 📰 How Many Bottles Of Water Equals A Gallon 1444895 📰 Pho Ben Noodle House Exposed Its Most Secrets You Wont Want To Watch 8012772 📰 The Shocking Truth About Salem Willows What Happens When History Meets Mystery 3757821 📰 How Long Does Lorazepam Stay In Your System 2860108 📰 You Wont Believe Whats In This Aol Portfolioyoure Going To Be Blown Away 5495966 📰 Did Elon Musk Resign From Doge 7697688 📰 Hsa Card Misinformation Spreading Fastheres The Shocking Truth 5498306 📰 R2 C R Racc24 Z2 Racc24 Rightarrow R2 Z2 C R 8566815 📰 Master Date Calculations Like A Pro See How Many Hours Youre Wasting 6141788 📰 Homewood Suites Greenville Sc 7539001 📰 Women Skinny Dipping 2975988 📰 From Ducks To Stunning Viewsduckpark Is Now The Must See Spot Youve Been Searching For 1144092 📰 Only The Flip Master Can Deliver This Life Changing Multitool Youve Been Searching For 2428973 📰 Uamy Stock News 8659447 📰 Finally A Simple Way To Access Your Medicare Secondary Payer Portalsee How It Works 8994062