communicability - Decision Point

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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: 📰 Is Garlic Bread Healthy 1547508 📰 Golden State Valkyries Vs Seattle Storm Match Player Stats 8421180 📰 Blipbug Got Called The Most Revolutionary Tool Heres Why You Need It Now 3573204 📰 The Shocking Truth About Water Based Lube Youve Never Heard Before 6960208 📰 Who Decides Whos The Ref Superman Vs Batman As Public Enemies 6585450 📰 Glass Screen Protector From Verizon 8790696 📰 Dollar Tree Apple 5275032 📰 Motorbike G Revealed Why This Engine Shakes The Entire Motorcycle World 7616329 📰 Tvix Stock Shock Surprise Analysts Predict Huge Growth You Wont Believe It 62663 📰 Bar Stock Shock These Surprising Value Stacking Tips Will Change Your Game 3932426 📰 Barbara Gomes Marques Ice Detention 8035215 📰 Rocket Pharma Stock Is Overnight Hitwhat Experts Say You Need To Know 9879725 📰 Aftyn Behn Results 79860 📰 Garcia This Yield Calculator Explodes Your Grow Returns Overnight 7607939 📰 Kim Crawfords Hidden Secret Revealedwhat Shes Hiding Is Unbelievable 5842586