microsfot 365 - Parker Core Knowledge

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📰 Question: If \(\mathbf{u}\), \(\mathbf{v}\), and \(\mathbf{w}\) are unit vectors, find the maximum value of \(\mathbf{u} \cdot (\mathbf{v} + \mathbf{w})\). 📰 Solution: The dot product \(\mathbf{u} \cdot (\mathbf{v} + \mathbf{w}) = \mathbf{u} \cdot \mathbf{v} + \mathbf{u} \cdot \mathbf{w}\). Since \(\mathbf{u}\), \(\mathbf{v}\), and \(\mathbf{w}\) are unit vectors, each dot product is at most 1. The maximum occurs when \(\mathbf{u}\) aligns with both \(\mathbf{v}\) and \(\mathbf{w}\), i.e., \(\mathbf{v} = \mathbf{w} = \mathbf{u}\). Then \(\mathbf{u} \cdot (\mathbf{v} + \mathbf{w}) = 1 + 1 = 2\). 📰 \boxed{2}Question: What is the smallest four-digit number that is a multiple of the least common multiple of the numbers $12$ and $18$, and also divisible by the square of the smallest prime greater than $10$? 📰 Ready To Level Up These Exotic Games Science Titles Are Taking Over 2024 4502845 📰 Hipaa Law Secrets That No One Wants You To Miss Before Its Too Late Find Out Now 9764309 📰 Unlock Faster Excel Navigation With These Insane Alternating Row Color Tricks 6677162 📰 Bankruptcy Bombshell Top 10 Target Companies Facing Collapse In 2024 8652569 📰 Ambev Stock Breakout Why Investors Are Fueling A Massive Bull Run In 2024 8295373 📰 5Watch Your Best Races Live Play The Newest Car Race Game Online Now 4714482 📰 5 Platinum Etf Explosion Is This The Next Blockbuster Investment Opportunity 7202396 📰 Dollar Rand Shock Why This Currency Could Crush Your Wallet Overnight 1569065 📰 Bank Of America Open 3106582 📰 Unseen Jennifer Morrison The Nude Shock That Defies All Expectations 621300 📰 Dont Give Me Hope 2481964 📰 How The Dollar To Rupee Match Is Changing Every Investors Mind Today 6015241 📰 Eco Friendly Green Shorts That Double As Fashion Statementsget Yours Before Theyre Gone 3380256 📰 Who Wins The Financial Firefight Blackrock Vs Blackstone Explained In This Clickbaiter 3764806 📰 401K 2026 Contribution Limit Over 50 4815586