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Home » Second + Fourth = $2a = 10 \Rightarrow a = 5$ - AIKO, infinite ways to autonomy.

Second + Fourth = $2a = 10 \Rightarrow a = 5$ - AIKO, infinite ways to autonomy.

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Set \(h(t) = 0\): \(-5t^2 + 20t + 10 = 0\).

📌 Divide by -5: \(t^2 - 4t - 2 = 0\).

📌 Use quadratic formula: \(t = rac{4 \pm \sqrt{(-4)^2 - 4(1)(-2)}}{2} = rac{4 \pm \sqrt{16 + 8}}{2} = rac{4 \pm \sqrt{24}}{2} = rac{4 \pm 2\sqrt{6}}{2} = 2 \pm \sqrt{6}\).

📌 Take positive root: \(t = 2 + \sqrt{6} pprox 4.45\) seconds.

📌 #### \(2 + \sqrt{6}\)

📌 The sum of an infinite geometric series is 16, and the first term is 8. What is the common ratio?

📌 Formula: \(S = rac{a}{1 - r}\).

📌 \(16 = rac{8}{1 - r}\) â \(1 - r = rac{8}{16} = 0.5\) â \(r = 0.5\).

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