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Home » One World at the Brink: How Doom Is Already Unraveling Our Future! - AMAZONAWS

One World at the Brink: How Doom Is Already Unraveling Our Future! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Find the derivative of \( f(x) = 5x^4 - 3x^2 + 2x - 7 \).

📌 Derivative of \( 5x^4 \) is \( 20x^3 \).

📌 Derivative of \( -3x^2 \) is \( -6x \).

📌 Derivative of \( 2x \) is \( 2 \).

📌 Derivative of \( -7 \) is \( 0 \).

📌 So, \( f'(x) = 20x^3 - 6x + 2 \).

📌 #### \( 20x^3 - 6x + 2 \)

📌 The \( n \)-th term of a geometric sequence is given by \( a_n = a_1 \cdot r^{n-1} \).

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Divide both sides by $ \sqrt{3} $:
rac{1}{4}s^2 = 25 \Rightarrow s^2 = 100 \Rightarrow s = 10 ext{ cm}
The new side length is $ s + 4 = 14 $ cm. Compute the new area:
A_{ ext{new}} = rac{\sqrt{3}}{4}(14)^2 = rac{\sqrt{3}}{4} \cdot 196...
\Delta A = 49\sqrt{3} - 25\sqrt{3} = 24\sqrt{3} ext{ cm}^2
Thus, the area increases by $ oxed{24\sqrt{3}} $ cmÂ².
Question: Find the length of the longest altitude of a triangle with s...
Solution: First, compute the area using Heronâs formula. Let $ a = 7...
s = rac{7 + 10 + 13}{2} = 15
The area $ A $ is:

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