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how to connect apple pencil - Feedz API

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 A cylindrical tank with a radius of 3 meters is filled with water to a height of 5 meters. If the water is drained at a rate of 2 cubic meters per minute, how long will it take to completely empty the tank?

📌 The volume of the cylinder is given by \( \pi r^2 h = \pi imes 3^2 imes 5 = 45\pi \) cubic meters.

📌 At a rate of 2 cubic meters per minute, the time to empty is \( rac{45\pi}{2} pprox 70.6858 \) minutes.

📌 Rounding to the nearest whole number, it takes approximately 71 minutes.

📌 The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = rac{n}{2} (2a + (n-1)d) \). If the first term \( a = 3 \) and the common difference \( d = 5 \), find the sum of the first 10 terms.

📌 Using the formula, \( S_{10} = rac{10}{2} (2 imes 3 + (10-1) imes 5) \).

📌 Simplifying, \( S_{10} = 5 (6 + 45) = 5 imes 51 = 255 \).

📌 A quadratic function is given by \( f(x) = 2x^2 - 4x + 1 \). Find the vertex of the parabola.

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