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Home » Divide by -5: \(t^2 - 4t - 2 = 0\). - 500apps

Divide by -5: \(t^2 - 4t - 2 = 0\). - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Subtracting these:

📌 $ 18a + 2b = 18 $ → $ 9a + b = 9 $

📌 Subtracting: $ 3a = 5 $ → $ a = \frac{5}{3} $, $ b = -6 $. Then $ c = \frac{43}{3} $, $ d = -15 $. Thus,

📌 g(x) = \dfrac{5}{3}x^3 - 6x^2 + \dfrac{43}{3}x - 15.

📌 Substitute $ x^2 - 1 $:

📌 g(x^2 - 1) = \dfrac{5}{3}(x^2 - 1)^3 - 6(x^2 - 1)^2 + \dfrac{43}{3}(x^2 - 1) - 15.

📌 \boxed{\dfrac{5}{3}x^6 - 5x^4 + \dfrac{50}{3}x^2 - 18}.

📌 $$Question: A particle physicist models the trajectory of a neutrino through a detector as the line $ y = \frac{3}{4}x + 2 $. Find the point on this trajectory that is closest to the detector's origin $ (0, 0) $.

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