MathDB

2

Part of 2014 BMT Spring

Problems(6)

BMT 2014 Spring - Geometry 2

Source:

12/29/2021
Regular hexagon ABCDEFABCDEF has side length 22 and center OO. The point PP is defined as the intersection of ACAC and OBOB. Find the area of quadrilateral OPCDOPCD.
geometry
2014 BMT Team 2

Source:

1/6/2022
A mathematician is walking through a library with twenty-six shelves, one for each letter of the alphabet. As he walks, the mathematician will take at most one book off each shelf. He likes symmetry, so if the letter of a shelf has at least one line of symmetry (e.g., M works, L does not), he will pick a book with probability 12\frac12. Otherwise he has a 14\frac14 probability of taking a book. What is the expected number of books that the mathematician will take?
combinatorics
BMT 2014 Spring - Analysis 2

Source:

1/6/2022
Find the smallest positive value of xx such that x3−9x2+22x−16=0x^3-9x^2+22x-16=0.
algebraPolynomials
BMT 2013 Spring - Discrete 2

Source:

1/6/2022
If I roll three fair 44-sided dice, what is the probability that the sum of the resulting numbers is relatively prime to the product of the resulting numbers?
probabilitycombinatorics
area of ABC wanted AB=EF, BC=FD, CA=DE=2. 2014 BMT Individual 3

Source:

1/2/2022
Suppose △ABC \vartriangle ABC is similar to △DEF\vartriangle DEF, with A A, B B, and CC corresponding to D,ED, E, and FF respectively. If AB‾=EF‾\overline{AB} = \overline{EF}, BC‾=FD‾\overline{BC} = \overline{FD}, and CA‾=DE‾=2\overline{CA} = \overline{DE} = 2, determine the area of △ABC \vartriangle ABC.
geometryarea of a triangleareas
BMT 2014 Spring - Discrete 2

Source:

1/6/2022
Find the number of 55-digit nn, s.t. every digit of nn is either 00, 11, 33, or 44, and nn is divisible by 1515.
combinatorics