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Two points are placed randomly along the circumference of a circle. What is the probability that the chord drawn between them is longer than the radius of the circle?
How often is Length of Chord > Radius?
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A positive integer n has d positive divisors.
After doubling n, you find that 2n has 2d positive divisors.
Is it possible that after tripling n, you will find that 3n has 3d positive divisors?
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The atmosphere is a layer of gas that surrounds our planet and is several hundred kilometers thick. Its main components are nitrogen, oxygen, argon, and water vapor.
What is the approximate mass m of the entire Earth's atmosphere?
Details and Assumptions:
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Define the star operation as a⋆b=a+ab+b.
Then define the star power operation as a⋆n=awrittenntimesa⋆a⋆a⋆⋯⋆a, with a⋆1=a.
What is 7⋆7?
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An equilateral triangle and 2 other regular polygons share a single vertex in such a way that the three shapes completely cover the 360∘ of space surrounding the vertex without overlapping.
What is the largest possible number of sides that one of the regular polygons can have?
An equilateral triangle, regular 9-gon, and regular 18-gon can cover all 360∘ around a single vertex. Is 18 the maximum number of sides one of these regular polygons can have?
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