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Home » Now compute the number of ways for each case using combinations: - Dyverse

Now compute the number of ways for each case using combinations: - Dyverse

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Lila is coding a simulation of a falling object with air resistance. The object’s velocity increases according to v(t) = 4.9t − 0.1t² (in m/s). At what time does the object reach maximum velocity?

📌 Maximum velocity occurs when dv/dt = 0 → dv/dt = 4.9 − 0.2t = 0 → t = 4.9 / 0.2 = <<4.9/0.2=24.5>>24.5 seconds

📌 Jordan, an aerospace intern, is analyzing the trajectory of a projectile launched at 60 m/s at 30° above horizontal. Ignoring air resistance, what is the maximum height reached? (Use g = 9.8 m/s²)

📌 Initial vertical velocity = 60 × sin(30°) = 60 × 0.5 = <<60*0.5=30>>30 m/s

📌 At max height, v = 0 → use v² = u² − 2gh → 0 = 30² − 2×9.8×h → h = 900 / 19.6 ≈ <<900/19.6=45.92>>45.92 m

📌 #### 45.92

📌 Elena, a physics student, is measuring the resonance frequency of a wire. She finds that tension F increases the frequency f according to f = (1/2L)√(F/μ), where L = 0.5 m, μ = 0.002 kg/m. If F increases from 40 N to 90 N, by how much does f increase?

📌 Base frequency: f₀ = (1/(2×0.5))√(40/0.002) = 1 × √(20000) ≈ <<sqrt(20000)=141.42>>141.42 Hz

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