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Home » L = \frac13 \times 2\pi \times 15 = 10\pi \text meters - Dyverse

L = \frac13 \times 2\pi \times 15 = 10\pi \text meters - Dyverse

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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 \( c \).

📌 Solution:** We are given the quadratic function \( P(x) = ax^2 + bx + c \) and the points \( P(1) = 6 \), \( P(2) = 11 \), and \( P(3) = 18 \). We can set up the following system of equations by substituting the known values:

📌 \( a(1)^2 + b(1) + c = 6 \) which simplifies to \( a + b + c = 6 \).

📌 \( a(2)^2 + b(2) + c = 11 \) which simplifies to \( 4a + 2b + c = 11 \).

📌 \( a(3)^2 + b(3) + c = 18 \) which simplifies to \( 9a + 3b + c = 18 \).

📌 Now, we solve this system of equations. Start with the first two equations:

📌 a + b + c &= 6 \quad \text{(Equation 1)} \\

📌 4a + 2b + c &= 11 \quad \text{(Equation 2)}

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