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Home » Thus, the area of the region covered by the dialect is $\boxed144\pi$. - Carbonext

Thus, the area of the region covered by the dialect is $\boxed144\pi$. - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 5A science communicator is filming a demonstration involving a projectile launched at an angle. The projectile's height in meters is modeled by the equation $ h(t) = -5t^2 + 20t + 10 $, where $ t $ is time in seconds. At what time does the projectile reach its maximum height?

📌 To find the time at which maximum height is reached, use the vertex formula $ t = -\frac{b}{2a} $ for the quadratic equation $ h(t) = -5t^2 + 20t + 10 $.

📌 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 $.

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