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Home » ight) = 4\left(rac32 - Dachbleche24

ight) = 4\left(rac32 - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Also: \( rac{1}{2} \cdot 4 \cdot h = 2h \).

📌 Set equal: \( 2h = rac{1}{2} \sqrt{55} \) â \( h = rac{\sqrt{55}}{4} \).

📌 #### \(rac{\sqrt{55}}{4}\)Question: Let $ f(u) = u - rac{u^4}{4} $ for every real number $ u $. If $ b_1 = 2 $ and $ b_{n+1} = f(b_n) $ for $ n \geq 1 $, find $ b_3 $.

📌 Solution: Compute $ b_2 = f(2) = 2 - rac{2^4}{4} = 2 - rac{16}{4} = 2 - 4 = -2 $. Then $ b_3 = f(-2) = -2 - rac{(-2)^4}{4} = -2 - rac{16}{4} = -2 - 4 = -6 $. Thus, $ b_3 = oxed{-6} $.

📌 Question: A science communicator designs an exhibit where the number of interactive stations $ S $ at time $ t $ (in hours) satisfies $ S(t) = t^2 - 5t + 6 $. Find all times $ t $ when $ S(t) = 0 $.

📌 Solution: Solve $ t^2 - 5t + 6 = 0 $. Factor: $ (t - 2)(t - 3) = 0 $. The solutions are $ t = 2 $ and $ t = 3 $. Thus, the times are $ oxed{2} $ and $ oxed{3} $.

📌 Question: A mammalogist models the population of a species using the functional equation $ h(x + y) = h(x) + h(y) + xy $ for all real $ x, y $. Find all functions $ h: \mathbb{R} o \mathbb{R} $.

📌 Solution: Assume $ h(x) = ax^2 + bx + c $. Substitute into the equation:

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