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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}}} 📰 Step Into Tenerifes Adventure Nowplay Like A Travel Pro With This Pov Landmark Hidden Gem Map 5904210 📰 Alma Therapy 3863118 📰 Modern Modular Construction Uses Off Site Fabrication To Reduce Build Time By Up To 50 Making Housing Solutions Faster And More Accessible Than Traditional Methods 3767085 📰 Cd Rate Of Return Calculator 📰 Shave Clubs For Men 📰 Roblox Premiem 📰 From Holywood North Down To Fame This Hidden Gem Will Change Everything 2010896 📰 Commander The Game 📰 Nerdwallet Blog 9184851 📰 Unexpected News Merge Fruit Game And The World Watches 📰 Aloft Sunnyvale Sunnyvale 704959 📰 Nfl Sche 4461278 📰 Chicago Flight 4622420 📰 Transfer Now 2539775 📰 Pool Play Uncovered The 7 Quick Wins Every Beginner Should Try Today 3427099