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Home » Question:** The radius of a sphere is tripled. By what factor does the volume increase? - ToelettAPP

Question:** The radius of a sphere is tripled. By what factor does the volume increase? - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \ln(2) + t \ln(1.05) = \ln(3) + t \ln(1.03)

📌 Solve for $ t $:

📌 t (\ln(1.05) - \ln(1.03)) = \ln(3) - \ln(2)

📌 t = \frac{\ln(3) - \ln(2)}{\ln(1.05) - \ln(1.03)}

📌 t = \frac{\ln\left(\frac{3}{2}\right)}{\ln\left(\frac{1.05}{1.03}\right)} \approx \frac{0.4055}{0.0198} \approx 20.48

📌 Since $ t $ must be a whole number, round up to the next month:

📌 \boxed{21}

📌 Question:** A geographer is studying elevation data and finds that the elevation at Point A is modeled by $ h(x) = 3x^2 - 6x + 5 $, and at Point B by $ k(x) = 2x^2 - 4x + m $. If the elevation at $ x = 2 $ is the same for both points, what is the value of $ m $?

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