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Home » \boxed5\pi\sqrt2 - jntua results

\boxed5\pi\sqrt2 - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 The sample is approximately 8679 years old.

📌 A civil engineer models traffic flow on a highway using the equation $v(x) = 80 - 0.5x^2$, where $v$ is speed in km/h and $x$ is distance in km from a bottleneck. What is the average speed from $x = 0$ to $x = 4$ km?

📌 Average speed = $rac{1}{4 - 0} \int_0^4 (80 - 0.5x^2) dx$.

📌 Compute integral: $\int_0^4 80\,dx - 0.5 \int_0^4 x^2\,dx = [80x]_0^4 - 0.5 \left[rac{x^3}{3}

📌 ight]_0^4 = 320 - 0.5 \cdot rac{64}{3} = 320 - rac{32}{3} = rac{960 - 32}{3} = rac{928}{3}$.

📌 Average = $rac{1}{4} \cdot rac{928}{3} = rac{928}{12} = 77.\overline{3}$.

📌 The average speed is $77rac{1}{3}$ km/h.

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