MathDB

8

Part of 2017 BMT Spring

Problems(5)

BMT 2017 Spring - Geometry 8

Source:

12/30/2021
Given a circle of radius 2525, consider the set of triangles with area at least 768768. What is the area of the intersection of all the triangles in this set?
geometry
2017 BMT Team 8

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1/6/2022
A function ff with its domain on the positive integers N={1,2,...}N =\{1, 2, ...\} satisfies the following conditions: (a) f(1)=2017f(1) = 2017. (b) ∑i=1nf(i)=n2f(n)\sum_{i=1}^n f(i) = n^2f(n), for every positive integer n>1n > 1. What is the value of f(2017)f(2017)?
algebra
2017 BMT Individual 8

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1/9/2022
If xy=15xy = 15 and x+y=11x + y = 11, calculate the value of x3+y3x^3 + y^3.
algebra
2017 BMT Discrete #8

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3/9/2024
In a 10241024 person randomly seeded single elimination tournament bracket, each player has a unique skill rating. In any given match, the player with the higher rating has a 34\frac34 chance of winning the match. What is the probability the second lowest rated player wins the tournament?
combinatorics
2017 BMT Analysis #8

Source:

3/10/2024
The numerical value of the following integral ∫01(−x2+x)2017⌊2017x⌋dx\int^1_0 (-x^2 + x)^{2017} \lfloor 2017x \rfloor dx can be expressed in the form am!2n!a\frac{m!^2}{ n!} where a is minimized. Find a+m+na + m + n. (Note ⌊x⌋\lfloor x\rfloor is the largest integer less than or equal to x.)
calculusintegrationfloor functionalgebra