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📰 Solution: The closest point minimizes distance. Parametrize the line as $ (t, 2t + 1) $. The squared distance to $ (3, 4) $ is $ (t - 3)^2 + (2t + 1 - 4)^2 = (t - 3)^2 + (2t - 3)^2 $. Differentiate: $ 2(t - 3) + 8t - 12 = 0 \Rightarrow 10t - 18 = 0 \Rightarrow t = 1.8 $. Substituting, the point is $ (1.8, 4.6) $. oxed{(1.8,\ 4.6)} 📰 Question: Find the maximum value of $ (\sin x + 2\cos x)^2 + \sin^2 x $. 📰 Solution: Expand $ (\sin x + 2\cos x)^2 = \sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Add $ \sin^2 x $: total $ 2\sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Simplify using identities: $ 2(1 - \cos^2 x) + 2\sin 2x + 4\cos^2 x = 2 + 2\cos^2 x + 2\sin 2x $. Let $ u = \cos^2 x $, $ \sin 2x = 2\sin x \cos x $. Alternatively, rewrite original expression as $ \sin^2 x + 4\sin x \cos x + 4\cos^2 x + \sin^2 x = 2\sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Let $ f(x) = 2\sin^2 x + 4\sin x \cos x + 4\cos^2 x $. Use $ \sin^2 x = rac{1 - \cos 2x}{2} $, $ \cos^2 x = rac{1 + \cos 2x}{2} $, $ \sin x \cos x = rac{\sin 2x}{2} $: 📰 This 2000 Rm To Usd Exchange Rate Changed Everythingworth Millions Today 9841339 📰 Amy Robach And Tj Holmes 978190 📰 Uc Michigan Patients Secret Unlock Instant Access To Your Medical Records Via The Umich Portal 1090673 📰 Why Yahoos Latest Coverage Shows The Nasdaq Composite Is Set For Massive Gains 1990987 📰 Kick Return Man 2 Breaks Recordswhat Would Happen If He Joined Your Team 1434019 📰 What Are Sticky Keys The Shocking Truth Youve Never Seen Before 345785 📰 Ampg Stock Price Is Soaringcan This Energy Giant Break 100 In 2025 9884120 📰 You Wont Trust Nairaland Again After This Unbelievable Shock 6279858 📰 Why Everyones Obsessed With The Color Gameheres What You Need To Know 6073784 📰 Type Like A Pro Unlock The Fastest Emoji Shortcut Online 8074639 📰 Fred Flinvstone Exposed The Hilarious Backstory That Defines Swann County 9929890 📰 You Wont Believe Which Games Spark The Most Unbelievable Funstart Playing Now 6406308 📰 6 Converting Dc Power To Ac Power In Substations 511417 📰 Why Everyones Obsessed With Comic K You Need To Watch This Now 1333616 📰 Mens Wedding Attire For Beach 8992572