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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: 📰 Why Boomtown Tourists Swarm These Hidden Gems Warming Up Near Knotts Berry Farm 📰 Why Cashmere Dries Like Paperunless You Follow This Secret Step 📰 Why Cheese Knives Work Better Than A Knife When Cutting Mangoyou Must Try This 📰 Why Cow Stomachs Are Full Of Surprises You Didnt Expectget Ready To Shock 📰 Why Dealers Wont Tell You Essential Secret Inside The Hyundai Accent That Saved Billions 📰 Why Did I Let It All Go The Truth Behind My Lyric Abandonment 📰 Why Did The Committee Silence Campus Grievances For Years 📰 Why Did You Ignore Them Hell O Dollies Rise Again 📰 Why Do So Many People Get Acai Wrong The Truth Will Surprise You 📰 Why Do We Accidentally Browse More Than We Think The Hidden Frequency You Never Saw 📰 Why Doctors Fear Immature Granulocytes Beneath The Surfaceshocking Truth Revealed 📰 Why Doctors Hate This Simple Ears Pop Trickyour Skeleton Will Thanks 📰 Why Doctors Wont Tell You The One Trick That Makes Hand Pain Vanish In Seconds 📰 Why Does Ice On Black Set The Streets Ablaze With Desire 📰 Why Electric Bat Sketches Suddenly Look Livestep By Step Magic Revealed