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Home » \frac2701140 = \frac938 - Imagemakers

\frac2701140 = \frac938 - Imagemakers

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 + 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 $?

📌 Solution: We are given $ D(t) = kt^2 + 5t $ and that $ D(3) = 48 $. Substituting $ t = 3 $:

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