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Home » This is a telescoping series. Write out the terms: - Groen Casting

This is a telescoping series. Write out the terms: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 P = 30 + 10\pi

📌 Thus, the perimeter is \(\boxed{30 + 10\pi \text{ meters}}\).Question: A palynologist observes that the number of pollen grains in a sample grows quadratically over time. If on day 2 there are 120 grains, on day 4 there are 360 grains, and on day 6 there are 720 grains, find the quadratic polynomial $ p(t) $ that models the number of pollen grains on day $ t $.

📌 Solution: Let $ p(t) = at^2 + bt + c $. Using the given data:

📌 $ p(2) = 4a + 2b + c = 120 $

📌 $ p(4) = 16a + 4b + c = 360 $

📌 $ p(6) = 36a + 6b + c = 720 $

📌 $$ (16a + 4b + c) - (4a + 2b + c) = 360 - 120 \Rightarrow 12a + 2b = 240 \Rightarrow 6a + b = 120 \quad \text{(i)} $$

📌 Subtracting equation (2) from (3):

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