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Average Door Size Explained: Stop Wasting Money on Wrong Door Dimensions! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Final answer: \(\boxed{(x - 2y)(x + 2y)(x^2 + 4y^2)}\)

📌 A sequence of five real numbers forms an arithmetic progression, and the sum of the squares of the terms is 1100. If the common difference is 3 and the middle term is 2, what is the first term?

📌 a - 6, \quad a - 3, \quad a, \quad a + 3, \quad a + 6

📌 Since the middle term is given as 2, we have \(a = 2\).

📌 So the terms are:

📌 -4, \quad -1, \quad 2, \quad 5, \quad 8

📌 Now compute the sum of the squares:

📌 This matches the given sum. Therefore, the first term is \(\boxed{-4}\).**Question:** A palynologist is analyzing pollen concentration data and models the relationship using a quadratic function. If the pollen concentration \( P(x) \) over time \( x \) is given by \( P(x) = ax^2 + bx + c \), and it's known that \( P(1) = 6 \), \( P(2) = 11 \), and \( P(3) = 18 \), determine the values of \( a \), \( b \), and \( c \).

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