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Home » You Won’t Believe This Joker Villain—Guarding Gotham’s Most Mad Genius! - Silent Sales Machine

You Won’t Believe This Joker Villain—Guarding Gotham’s Most Mad Genius! - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 An entomologist is studying insect pollination and models the number of flowers \( F \) pollinated by bees as a quadratic function of time \( t \) in hours: \( F(t) = pt^2 + qt + r \). If 15 flowers are pollinated after 1 hour, 40 after 2 hours, and 75 after 3 hours, determine the values of \( p \), \( q \), and \( r \).

📌 To find \( p \), \( q \), and \( r \), use the given conditions in the quadratic equation \( F(t) = pt^2 + qt + r \).

📌 For \( t = 1 \), \( F = 15 \):

📌 p(1)^2 + q(1) + r = 15 \quad \Rightarrow \quad p + q + r = 15 \quad \text{(Equation 1)}

📌 For \( t = 2 \), \( F = 40 \):

📌 p(2)^2 + q(2) + r = 40 \quad \Rightarrow \quad 4p + 2q + r = 40 \quad \text{(Equation 2)}

📌 For \( t = 3 \), \( F = 75 \):

📌 p(3)^2 + q(3) + r = 75 \quad \Rightarrow \quad 9p + 3q + r = 75 \quad \text{(Equation 3)}

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This is an arithmetic series where each term increases by a constant d...
Number of Episodes (n):** 12
First Episode Duration (a₁):** 15 minutes
Common Difference (d):** 10 minutes
The duration of each episode forms an arithmetic sequence:
15, 25, 35, \ldots
The \(n\)-th term of an arithmetic sequence is:
a_n = a_1 + (n - 1)d
Calculate the duration of the 12th episode:
a_{12} = 15 + (12 - 1) \times 10 = 15 + 110 = 125 \text{ minutes}

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