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Home » D. It is consumed during the reaction and regenerated in the final step. - Tacotoon

D. It is consumed during the reaction and regenerated in the final step. - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question:** An environmental engineer is evaluating 6 different renewable energy sources. In how many ways can she select a subset of at least 2 and at most 5 sources to pilot in a new solar-wind hybrid system?

📌 We are to compute the number of subsets of a 6-element set with size between 2 and 5, inclusive.

📌 The number of subsets of size \( k \) is \( \binom{6}{k} \). So we compute:

📌 \binom{6}{2} + \binom{6}{3} + \binom{6}{4} + \binom{6}{5}

📌 Calculate each term:

📌 \binom{6}{2} = 15, \quad \binom{6}{3} = 20, \quad \binom{6}{4} = 15, \quad \binom{6}{5} = 6

📌 + 20 + 15 + 6 = 56

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\[ f(u) = (u - 1)^2 Q(u) + au + b \]
\( f(1) = a(1) + b = a + b \)
Differentiate: \( f'(u) = 2(u - 1)Q(u) + (u - 1)^2 Q'(u) + a \), so \(...
Compute \( f(1) \):
\[ f(1) = 1^5 - 3(1)^3 + 2(1) + 8 = 1 - 3 + 2 + 8 = 8 \]
\[ a + b = 8 \quad ext{(1)} \]
Compute \( f'(u) \):
\[ f'(u) = 5u^4 - 9u^2 + 2 \]
\[ f'(1) = 5(1)^4 - 9(1)^2 + 2 = 5 - 9 + 2 = -2 \]
\[ a = -2 \]

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