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Home » Model: P(t) = P₀e^(rt). - Portal da AcÃºstica

Model: P(t) = P₀e^(rt). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A cylindrical tank with a radius of 3 meters is filled with water to a height of 10 meters. If the tank is emptied at a rate of 2 cubic meters per minute, how long will it take to completely empty the tank?

📌 The volume \( V \) of the cylinder is given by:

📌 V = \pi r^2 h = \pi \times 3^2 \times 10 = 90\pi \text{ cubic meters}

📌 At a rate of 2 cubic meters per minute, the time \( t \) to empty the tank is:

📌 t = \frac{90\pi}{2} = 45\pi \text{ minutes}

📌 Approximating \(\pi \approx 3.14\):

📌 t \approx 45 \times 3.14 = 141.3 \text{ minutes}

📌 A quadratic equation \( ax^2 + bx + c = 0 \) has roots \( \alpha \) and \( \beta \). If \( a = 2 \), \( b = -7 \), and \( c = 3 \), find the sum and product of the roots.

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