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Home » "One Fine Day", a line from the song "Sympathy for the Devil" in The Beatles' film Help! - 500apps

"One Fine Day", a line from the song "Sympathy for the Devil" in The Beatles' film Help! - 500apps

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 A ball is thrown upward with an initial velocity of 20 m/s from a height of 5 meters. Its height after \( t \) seconds is modeled by \( h(t) = -5t^2 + 20t + 5 \). When does the ball hit the ground?

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

📌 Divide by -5: \( t^2 - 4t - 1 = 0 \).

📌 Using the quadratic formula: \( t = \frac{4 \pm \sqrt{16 + 4}}{2} = \frac{4 \pm \sqrt{20}}{2} = \frac{4 \pm 2\sqrt{5}}{2} = 2 \pm \sqrt{5} \).

📌 Since time must be positive, \( t = 2 + \sqrt{5} \approx 4.24 \) seconds.

📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = \frac{n}{2}(2a + (n-1)d) \). If the sum of the first 10 terms is 150 and the first term is 5, what is the common difference \( d \)?

📌 Substitute \( n = 10 \), \( S_{10} = 150 \), \( a = 5 \):

📌 \( 150 = \frac{10}{2}(2 \cdot 5 + 9d) = 5(10 + 9d) \).

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