MathDB

5

Part of 2022 BMT

Problems(5)

BMT 2022 Fall Algebra P5

Source:

5/5/2023
For real numbers B,M,B,M, and T,T, we have B2+M2+T2=2022B^2+M^2+T^2 =2022 and B+M+T=72.B+M+T =72. Compute the sum of the minimum and maximum possible values of T.T.
algebra
BMT 2022 Fall Discrete P5

Source:

5/6/2023
Given a positive integer n,n, let s(n)s(n) denote the sum of the digits of n.n. Compute the largest positive integer nn such that n=s(n)2+2s(n)−2.n = s(n)^2 + 2s(n) - 2.
number theoryDiscrete
BMT 2022 Geometry #5

Source:

8/12/2023
Steve has a tricycle which has a front wheel with a radius of 3030 cm and back wheels with radii of 1010 cm and 99 cm. The axle passing through the centers of the back wheels has a length of 4040 cm and is perpendicular to both planes containing the wheels. Since the tricycle is tilted, it goes in a circle as Steve pedals. Steve rides the tricycle until it reaches its original position, so that all of the wheels do not slip or leave the ground. The tires trace out concentric circles on the ground, and the radius of the circle the front wheel traces is the average of the radii of the other two traced circles. Compute the total number of degrees the front wheel rotates. (Express your answer in simplest radical form.)
geometry
BMT 2022 Guts #5

Source:

8/31/2023
Theo and Wendy are commuting to school from their houses. Theo travels at xx miles per hour, while Wendy travels at x+5x + 5 miles per hour. The school is 44 miles from Theo’s house and 1010 miles from Wendy’s house. If Wendy’s commute takes double the amount of time that Theo’s commute takes, how many minutes does it take Wendy to get to school?
algebra
BMT 2022 Fall General P5

Source:

5/7/2023
Compute the last digit of (520+2)3.(5^{20}+2)^3.
number theory