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Home » p^3 + q^3 = (p + q)^3 - 3pq(p + q) - Silent Sales Machine

p^3 + q^3 = (p + q)^3 - 3pq(p + q) - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 The projectile reaches its maximum height at $ t = 2 $ seconds.

📌 A seismologist analyzing earthquake data observes that the amplitude of seismic waves increases exponentially by 15% every 2 seconds. If the initial amplitude is 40 units, what will the amplitude be after 10 seconds?

📌 The growth follows the formula $ A = A_0(1 + r)^t $, where $ r = 0.15 $ per 2 seconds, and $ t = \frac{10}{2} = 5 $ intervals.

📌 So, $ A = 40(1.15)^5 $.

📌 Calculating: $ 1.15^5 \approx 2.011357 $, so $ A \approx 40 \times 2.011357 = 80.45428 $.

📌 Rounding to two decimal places, the amplitude is approximately 80.45 units.

📌 #### 80.45

📌 A theoretical physicist explains that a certain virtual particle fluctuates in energy according to the function $ E(t) = 3\sin(2\pi t) + 4 $, where $ t $ is in nanoseconds. What is the average energy of the particle over one full cycle?

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