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Home » D) $ A = r + s $ - Rice University

D) $ A = r + s $ - Rice University

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 Solution: Let $ h $ represent the number of hours worked. The total fee for the first consultant is $ 300 + 75h $, and for the second consultant it is $ 200 + 90h $. Setting these equal:

📌 + 75h = 200 + 90h

📌 Subtract $ 75h $ and $ 200 $ from both sides:

📌 Divide both sides by 15:

📌 h = \frac{100}{15} = \frac{20}{3}

📌 Thus, the total fees are equal after $ \boxed{\frac{20}{3}} $ hours.

📌 Question: A materials scientist in Brazil is developing a bio-based plastic that degrades at a rate proportional to the square of the time in weeks, $ t^2 $. The degradation function is modeled as $ D(t) = kt^2 + 5t $, where $ k $ is a constant. If after 3 weeks, the degradation is measured at 48 grams, what is the value of $ k $?

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