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Home » You’ll Be SHOCKED: Chinese Donuts Are Takeover Ready – Watch What’s Next! - High Altitude Science

You’ll Be SHOCKED: Chinese Donuts Are Takeover Ready – Watch What’s Next! - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The value of $ a $ is $ \boxed{100} $.

📌 Question: Rationalize the denominator of $ \frac{\sqrt{7}}{\sqrt{7} - \sqrt{3}} $.

📌 Solution: Multiply numerator and denominator by the conjugate $ \sqrt{7} + \sqrt{3} $:

📌 \frac{\sqrt{7}(\sqrt{7} + \sqrt{3})}{(\sqrt{7} - \sqrt{3})(\sqrt{7} + \sqrt{3})} = \frac{7 + \sqrt{21}}{7 - 3} = \frac{7 + \sqrt{21}}{4}

📌 The rationalized form is $ \boxed{\dfrac{7 + \sqrt{21}}{4}} $.

📌 Question: The functions $ f(x) = x^2 - 6x + m $ and $ g(x) = x^2 - 6x + 3m $ are evaluated at $ x = 5 $. If $ f(5) = 2g(5) $, find $ m $.

📌 Solution: Compute $ f(5) = 25 - 30 + m = -5 + m $ and $ g(5) = 25 - 30 + 3m = -5 + 3m $.

📌 Set $ f(5) = 2g(5) $:

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