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Home » Equation: \( 2^x+1 = 2^4 \). - Portal da AcÃºstica

Equation: \( 2^x+1 = 2^4 \). - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solution: First, compute the area using Heronâs formula. Let $ a = 7 $, $ b = 10 $, $ c = 13 $. The semi-perimeter $ s $ is:

📌 s = rac{7 + 10 + 13}{2} = 15

📌 The area $ A $ is:

📌 A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{15(15 - 7)(15 - 10)(15 - 13)} = \sqrt{15 \cdot 8 \cdot 5 \cdot 2} = \sqrt{1200}

📌 \sqrt{1200} = \sqrt{100 \cdot 12} = 10\sqrt{12} = 10 \cdot 2\sqrt{3} = 20\sqrt{3} ext{ cm}^2

📌 The altitude $ h $ corresponding to a side $ b $ is given by:

📌 A = rac{1}{2} b h \Rightarrow h = rac{2A}{b}

📌 To find the longest altitude, we use the shortest side, since altitude is inversely proportional to the base. The shortest side is $ 7 $ cm.

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First, expand \( (t+1)^2 \):
Now substitute back:
f(t+1) = 3(t^2 + 2t + 1) + 5(t+1) + 2
Distribute each term:
= 3t^2 + 6t + 3 + 5t + 5 + 2
= 3t^2 + 11t + 10
The expanded expression is:
\boxed{3t^2 + 11t + 10}
Question:** A nanotechnologist is analyzing the behavior of a nanopart...
To rationalize the denominator, multiply the numerator and the denomin...

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