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Home » Subtract 2 constant sequences → \(30\) - Tacotoon

Subtract 2 constant sequences → \(30\) - Tacotoon

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 $$ 5x + 1 = x^2 + x - 2 $$

📌 Bring all terms to one side:

📌 $$ 0 = x^2 - 4x - 3 $$

📌 $$ x = \frac{4 \pm \sqrt{16 + 12}}{2} = \frac{4 \pm \sqrt{28}}{2} = 2 \pm \sqrt{7} $$

📌 The solutions are $ \boxed{2 + \sqrt{7}} $ and $ \boxed{2 - \sqrt{7}} $.

📌 Question: Rationalize the denominator of $ \frac{\sqrt{5}}{\sqrt{3} - \sqrt{2}} $.

📌 Solution: Multiply numerator and denominator by $ \sqrt{3} + \sqrt{2} $:

📌 $$ \frac{\sqrt{5}(\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2})} $$

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Thus, the engagement score after 6 minutes is 19.
\boxed{19}Question: A meteorologist models the change in atmospheric p...
Solution: To find the local extrema of the function $ P(t) = t^3 - 6t^...
P'(t) = 3t^2 - 12t + 9.
Set $ P'(t) = 0 $ to find critical points:
3t^2 - 12t + 9 = 0 \Rightarrow t^2 - 4t + 3 = 0.
Factoring gives:
To determine the nature of these critical points, we use the second de...
P''(t) = 6t - 12.
Evaluate at the critical points:

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