MathDB

2.8 1.4

Part of 2021 CMIMC

Problems(3)

2021 Alg/NT Div 1 P4 (Div 2 P8)

Source:

3/2/2021
Let f(x)=x28f(x) = \frac{x^2}8. Starting at the point (7,3)(7,3), what is the length of the shortest path that touches the graph of ff, and then the xx-axis?
Proposed by Sam Delatore
algebra
2021 Geo Div 1 P4 (Div 2 P8)

Source:

3/2/2021
Let ABCDEFABCDEF be an equilateral heaxagon such that △ACE≅△DFB\triangle ACE \cong \triangle DFB. Given that AC=7AC = 7, CE=8CE=8, and EA=9EA=9, what is the side length of this hexagon?
Proposed by Thomas Lam
geometry
2021 Combo Div 1 P4 (Div 2 P8)

Source:

3/2/2021
Suppose you have a 66 sided dice with 33 faces colored red, 22 faces colored blue, and 11 face colored green. You roll this dice 2020 times and record the color that shows up on top. What is the expected value of the product of the number of red faces, blue faces, and green faces?
Proposed by Daniel Li
combinatorics