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$\boxed\dfrac10x - 43$ - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A sustainable materials researcher models the degradation rate of a biodegradable polymer with the function $ D(t) = rac{t^2 + 1}{t - 2} $. Find all vertical asymptotes and holes in the graph of $ D(t) $.

📌 Solution: To find vertical asymptotes and holes, we examine the denominator of $ D(t) = rac{t^2 + 1}{t - 2} $.

📌 t - 2 = 0 \Rightarrow t = 2

📌 Now check the numerator at $ t = 2 $:

📌 t^2 + 1 = 4 + 1 = 5

📌 Since the numerator is not zero when $ t = 2 $, and the denominator is zero, there is a vertical asymptote at $ t = 2 $. There are no common factors between numerator and denominator, so there are no holes.

📌 oxed{ ext{Vertical asymptote at } t = 2; ext{ no holes} }

📌 Question: A robotics engineer uses the function $ f(x) = \sqrt{x + 3} $ and $ g(x) = 2x - 1 $ to model sensor feedback and actuator response. What is the value of $ g(f(6)) $?

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