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Home » Why Your Mail Always Goes Lost—Get This Shocking Envelope Addressing Secret NOW! - Appcentric

Why Your Mail Always Goes Lost—Get This Shocking Envelope Addressing Secret NOW! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Total perimeter:

📌 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 $

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

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So \( b = 7c + 3 \), then:
N = 20(7c + 3) + 7 = 140c + 60 + 7 = 140c + 67
Smallest positive \( N \) when \( c = 0 \): \( N = 67 \)
Check all conditions:
\( 67 \div 4 = 16 \times 4 = 64 \), remainder 3 → ✓
\( 67 \div 5 = 13 \times 5 = 65 \), remainder 2 → ✓
\( 67 \div 7 = 9 \times 7 = 63 \), remainder 4 → ✓
Thus, the smallest such \( N \) is:
\boxed{67}
An ornithologist analyzing flight data finds that the number of daily...

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