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Home » How to Grow Cinnamon Hair Color Overnight: A Fast, Easy Step-by-Step Trouble-Free! - 500apps

How to Grow Cinnamon Hair Color Overnight: A Fast, Easy Step-by-Step Trouble-Free! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 y + \frac{1}{y} \geq 2

📌 Equality occurs when $y = 1$, i.e., $\tan x = 1 \Rightarrow x = \frac{\pi}{4}$.

📌 Thus, the minimum value is:

📌 + 2 = \boxed{9}

📌 Question: A regular tetrahedron has three of its vertices at $(0,0,0)$, $(1,1,0)$, and $(1,0,1)$. Find the coordinates of the fourth vertex, assuming all coordinates are integers.

📌 Let the fourth vertex be $(x, y, z)$, and recall that in a regular tetrahedron, all edges have equal length.

📌 Compute edge lengths between the known points:

📌 \text{Distance between } (0,0,0) \text{ and } (1,1,0): \sqrt{(1)^2 + (1)^2 + 0} = \sqrt{2} \\

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\( a=0, b=1 \): 5
\( a=1, b=1 \): 15
\( a=2, b=1 \): 45
Sum them:
+ 3 + 9 + 5 + 15 + 45 = 78
Thus, the sum of all odd divisors of 180 is \(\boxed{78}\).
Question:** A philosopher of science reflects on the elegance of symme...
Here, \( a = 10 \), \( b = 15 \), so:
\gcd(10, 15) = 5
\gcd(2^{10} - 1, 2^{15} - 1) = 2^5 - 1 = 32 - 1 = 31

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