MathDB

3

Part of 2015 BMT Spring

Problems(5)

BMT 2015 Spring - Geometry 3

Source:

12/30/2021
Let MM be on segmentBC BC of △ABC\vartriangle ABC so that AM=3AM = 3, BM=4BM = 4, and CM=5CM = 5. Find the largest possible area of △ABC\vartriangle ABC.
geometry
2015 BMT Team 3

Source:

1/6/2022
How many ways are there to place the numbers 2,3,...,102, 3, . . . , 10 in a 3×33 \times 3 grid, such that any two numbers that share an edge are mutually prime?
combinatorics
2015 BMT Spring Analysis 3

Source:

1/20/2022
Find all integer solutions to \begin{align*} x^2+2y^2+3z^2&=36,\\ 3x^2+2y^2+z^2&=84,\\ xy+xz+yz&=-7. \end{align*}
algebrasystem of equationsnumber theory
2015 BMT Spring Discrete 3

Source:

1/20/2022
How many rational solutions are there to 5x2+2y2=15x^2+2y^2=1?
number theory
BD^2=? <ABC=90^o,AB=12, BC=9,CD=20, DA=25, 2015 BMT Individual 3

Source:

1/3/2022
A quadrilateral ABCDABCD has a right angle at ∠ABC\angle ABC and satisfies AB=12AB = 12, BC=9BC = 9, CD=20CD = 20, and DA=25DA = 25. Determine BD2BD^2. .
geometryright angle