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Home » Given the instruction, and previous examples use exact decimals, we output: - Upplift

Given the instruction, and previous examples use exact decimals, we output: - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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Solution:** To verify if \( x = 1 \) is a root of multiplicity greater...
Calculate \( p(1) \):
p(1) = 1^4 - 4 imes 1^3 + 6 imes 1^2 - 4 imes 1 + 1 = 1 - 4 + 6 - 4...
Since \( p(1) = 0 \), \( x = 1 \) is indeed a root. To check the multi...
p'(x) = 4x^3 - 12x^2 + 12x - 4
Now, evaluate \( p'(1) \):
p'(1) = 4 imes 1^3 - 12 imes 1^2 + 12 imes 1 - 4 = 4 - 12 + 12 - 4...
Since \( p'(1) = 0 \), \( x = 1 \) is a root of multiplicity at least...
p''(x) = 12x^2 - 24x + 12
Evaluate \( p''(1) \):

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We now solve the system $ a + b = 35 $, $ a^2 + b^2 = 625 $. Use ident...
\Rightarrow 2ab = 600 \Rightarrow ab = 300
A = \frac{1}{2}ab = 150
Area of the inscribed circle:
A_{\text{circle}} = \pi r^2 = \pi \cdot 25 = 25\pi
\frac{A_{\text{circle}}}{A_{\text{triangle}}} = \frac{25\pi}{150} = \f...
Thus, the ratio is $ \boxed{\frac{\pi}{6}} $.Question: A plant biologi...
The rate of change of $ f(t) $ is given by its derivative:
f'(t) = -A\omega \sin(\omega t + \phi)
The maximum rate of change occurs when $ \sin(\omega t + \phi) = \pm 1...

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