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Home » Solution: By the Remainder Theorem, substitute $ n = 1 $ into $ P(n) $: - ClickBalance

Solution: By the Remainder Theorem, substitute $ n = 1 $ into $ P(n) $: - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 A student in the robotics STEM program is programming a drone to follow a trajectory defined by \(y = 2x^2 - 8x + 10\). What is the minimum altitude the drone reaches?

📌 The function is quadratic. Minimum occurs at vertex:

📌 \(x = -\frac{b}{2a} = -\frac{-8}{2 \cdot 2} = \frac{8}{4} = 2\)

📌 \(y = 2(2)^2 - 8(2) + 10 = 8 - 16 + 10 = 2\)

📌 Minimum altitude is 2 meters

📌 Dr. Kim is managing a portfolio of 12 research projects. If 3 projects are in biotech, 4 in renewable energy, and 5 in AI, and she selects 2 projects at random for a progress review, what is the probability both are AI-related?

📌 Total ways to choose 2 projects: \( \binom{12}{2} = \frac{12 \cdot 11}{2} = 66 \)

📌 Ways to choose 2 AI projects: \( \binom{5}{2} = \frac{5 \cdot 4}{2} = 10 \)

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