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Home » Acrylic Nail Tips: How Long Do They Really Last? The Answer Will Surprise You! - Upplift

Acrylic Nail Tips: How Long Do They Really Last? The Answer Will Surprise You! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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Solution: The volume of a sphere is given by $ V = \frac{4}{3} \pi r^3...
We are given that $ \frac{dV}{dt} = k \sin \theta $, and $ \theta = 60...
k \cdot \frac{\sqrt{3}}{2} = 4\pi r^2 \frac{dr}{dt}
Solving for $ \frac{dr}{dt} $:
\frac{dr}{dt} = \frac{k \sqrt{3}}{8\pi r^2}
The rate of volume increase is given directly as $ \frac{dV}{dt} = k \...
\frac{dV}{dt} = \frac{k\sqrt{3}}{2}
Thus, the rate of volume increase at $ \theta = 60^\circ $ is $ \boxed...
Question: A data analyst plots a triangle on a coordinate plane with s...
Solution: The triangle has side lengths $ a = 13 $, $ b = 14 $, and $...

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\text{LCM} = 2^3 \cdot 3^1 = 8 \cdot 3 = 24
Therefore, the least common multiple is \(\boxed{24}\).
Question: What is the smallest prime factor of 77?
Solution: To find the smallest prime factor of 77, we test divisibilit...
77 is odd, so it is not divisible by 2.
Sum of digits of 77 is \( 7 + 7 = 14 \), which is not divisible by 3,...
The last digit is not 0 or 5, so 77 is not divisible by 5.
Check divisibility by 7: \( 77 \div 7 = 11 \), which is an integer.
Thus, 77 is divisible by 7, and since 7 is a prime number, it is the s...
Therefore, the smallest prime factor is \(\boxed{7}\).

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