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Home » These 10 Legendary Pokémon Friends Are Changing the Game Forever! - 500apps

These 10 Legendary Pokémon Friends Are Changing the Game Forever! - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 = \frac{1}{2} + \frac{1}{4} - \frac{1}{2} - \frac{1}{51} + \frac{1}{2} \cdot \frac{1}{51} + \frac{1}{2} \cdot \frac{1}{52} = \frac{1}{4} - \frac{1}{102} + \frac{1}{104}.

📌 \frac{1}{4} - \frac{1}{102} + \frac{1}{104} = \frac{1}{4} - \frac{52 - 51}{5304} = \frac{1}{4} - \frac{1}{5304} = \frac{1326 - 1}{5304} = \frac{1325}{5304}.

📌 Final answer: $\boxed{\dfrac{1325}{5304}}$Question:

📌 A micropaleontologist is studying a circular microfossil with a radius of 5 cm. If a concentric circular groove of width 1 cm is carved through the center, what is the area of the remaining microfossil material in square centimeters?

📌 The original area of the circular microfossil is calculated using the formula for the area of a circle:

📌 where \( r = 5 \) cm. Thus, the original area is:

📌 A = \pi (5)^2 = 25\pi \text{ square centimeters.}

📌 The groove is 1 cm wide and concentric, effectively reducing the radius of the remaining material to \( 5 - 1 = 4 \) cm. The area of the reduced circle (remaining material) is:

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u^2 + 1 = 3u \Rightarrow u^2 - 3u + 1 = 0
So \( rac{a + b}{a - b} = rac{3 \pm \sqrt{5}}{2} \). Letâs take on...
rac{a + b}{a - b} = rac{3 + \sqrt{5}}{2}
2(a + b) = (3 + \sqrt{5})(a - b)
2a + 2b = (3 + \sqrt{5})a - (3 + \sqrt{5})b
2a - (3 + \sqrt{5})a + 2b + (3 + \sqrt{5})b = 0
\Rightarrow a(-1 - \sqrt{5}) + b(5 + \sqrt{5}) = 0
Solve for \( rac{a}{b} \):
a b ( -\overline{1 + \sqrt{5}} + (5 + \sqrt{5}) ) = 0 \Rightarrow -ra...
Let \( r = rac{a}{b} = rac{2x}{y} \), then:

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