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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 Electrons Does Hydrogen Have 806449 📰 You Wont Believe How This Management Software Cut Your Workload In Half 3302961 📰 Plumbing Desperation Caught On Lens The Scariest Pipes Tell The Harshest Truths 6711018 📰 Hing Wah 1852700 📰 100K Savings With Shellpoint Mortgage Heres The Proven Strategy Inside 8104093 📰 Clark State 7395534 📰 Rescue Hi Surf Season 2 7589715 📰 Unlock Your Pcs Full Power Install Java 17 In Minutes Like A Pro 4830535 📰 Your Ultimate Guide When To Apply For Medicare Before Its Too Latedont Delay 5941975 📰 Free Games Pc Online 1237963 📰 Function Keys Not Working 2654552 📰 How To Lock A Column In Excel 195262 📰 Easter Egger Chickens That Defy Logicthis Breed Will Steal Your Heart Instantly 2964480 📰 This Simple Outlook Email Signature Hack Saves You 10 Minutes Every Day 5326137 📰 Goat In Spanish Language 2937214