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Home » D: $a_n = 2^n \cdot 5 - 3 \cdot \frac2^n - 11$ - 500apps

D: $a_n = 2^n \cdot 5 - 3 \cdot \frac2^n - 11$ - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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Use chain rule: \( rac{dy}{dx} = rac{1}{x^2 + 1} \cdot 2x = rac{2x}...
Evaluate at \( x = 1 \): \( rac{2(1)}{1^2 + 1} = rac{2}{2} = 1 \).
The sum of an infinite geometric series is 12, and the first term is 3...
Sum formula: \( S = rac{a}{1 - r} \), so \( 12 = rac{3}{1 - r} \).
Solve: \( 12(1 - r) = 3 \) â \( 12 - 12r = 3 \) â \( 12r = 9 \) â...
A right triangle has legs of lengths \( \sqrt{5} \) and \( \sqrt{11} \...
Hypotenuse: \( c = \sqrt{(\sqrt{5})^2 + (\sqrt{11})^2} = \sqrt{5 + 11}...
Area: \( rac{1}{2} \cdot \sqrt{5} \cdot \sqrt{11} = rac{1}{2} \sqrt{...
Also: \( rac{1}{2} \cdot 4 \cdot h = 2h \).
Set equal: \( 2h = rac{1}{2} \sqrt{55} \) â \( h = rac{\sqrt{55}}{...

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