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Home » \mathbfa \times (\mathbfv \times \mathbfa) = \mathbfa \times \mathbfb - ClickBalance

\mathbfa \times (\mathbfv \times \mathbfa) = \mathbfa \times \mathbfb - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Here, $ a = -5 $, $ b = 20 $, so $ t = -\frac{20}{2(-5)} = \frac{20}{10} = 2 $.

📌 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

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