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Home » Number of ways: \(\binom43 = 4\) (choose 3 to go to the 3-element archive) - Portal da AcÃºstica

Number of ways: \(\binom43 = 4\) (choose 3 to go to the 3-element archive) - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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\( r + s + t = 6 \), \( rs + rt + st = 11 \), \( rst = 6 \)
\( r^2 + s^2 + t^2 = (r + s + t)^2 - 2(rs + rt + st) = 6^2 - 2(11) = 3...
Problem:** A triangle has sides of lengths 7, 8, and 9. What is its ar...
Use Heron’s formula.
Semi-perimeter \( s = \frac{7 + 8 + 9}{2} = 12 \)
Area \( A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{12(12 - 7)(12 - 8)(1...
Problem:** A geometric sequence has first term 3 and third term 27. Wh...
Let common ratio be \( r \).
\( a_1 = 3 \), \( a_3 = 3r^2 = 27 \Rightarrow r^2 = 9 \Rightarrow r =...
Sum \( S_5 = 3 \frac{3^5 - 1}{3 - 1} = \frac{3(243 - 1)}{2} = \frac{3...

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