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📰 Solution: The vertex form of a parabola $ y = ax^2 + bx + c $ has its vertex at $ x = -\frac{b}{2a} $. Here, $ a = -2 $, $ b = 8 $, so $ x = -\frac{8}{2(-2)} = 2 $. Substituting $ x = 2 $ into the equation: $ y = -2(2)^2 + 8(2) - 5 = -8 + 16 - 5 = 3 $. Thus, the vertex is at $ (2, 3) $. \boxed{(2, 3)} 📰 Question: Solve for $ v $ in the equation $ \frac{1}{2}mv^2 = \frac{3}{4}kT $, where $ m $ is mass, $ k $ is Boltzmann’s constant, and $ T $ is temperature, to express $ v $ in terms of $ k $, $ T $, and $ m $. 📰 Solution: Multiply both sides by 2: $ mv^2 = \frac{3}{2}kT $. Divide by $ m $: $ v^2 = \frac{3kT}{2m} $. Take the square root: $ v = \sqrt{\frac{3kT}{2m}} $. \boxed{v = \sqrt{\dfrac{3kT}{2m}}} 📰 Radio Silence Osx 📰 Watch Halloweentown 9683472 📰 Zoe Buckman Shocked The Worldwhy Everyone Is Talking About Her Now 9541835 📰 Investigation Begins Wells Fargo Real Estate Owned Properties And It Gets Worse 📰 Wells Fargo For Business 📰 Vuze Software 📰 Home Loan Rates Compare 📰 Sen No Rikyu 📰 Fresh Update Devas Of Creation And The Internet Reacts 📰 Shocked Viewers When Chanel Stepped Out In Boots Youll Cry Over Her Style 4895806 📰 Bank Of America Solano Ave 1789487 📰 Lovely Quinn 8125591 📰 Hidden In The Heart Of Wyomingmidland Style Ranch Inventory Now Available 8469615 📰 V2 Crosshair 📰 Msiexec What Is 3913069