MathDB

6

Part of 2017 ASDAN Math Tournament

Problems(5)

2017 Algebra #6

Source:

8/20/2022
If x+y−99=3x+y^{-99}=3 and x+y=−2x+y=-2, find the sum of all possible values of xx.
2016Algebra Test
2017 Calculus #6

Source:

9/17/2022
Compute lim⁡x→0cos⁡x5−cos⁡x3x2.\lim_{x\rightarrow0}\frac{\sqrt[5]{\cos x}-\sqrt[3]{\cos x}}{x^2}.
2017Calculus Test
2017 Discrete #6

Source:

10/12/2022
The sum ∑n=02016⋅201722018n\sum_{n=0}^{2016\cdot2017^2}2018^n can be represented uniquely in the form ∑i=0∞ai⋅2017i\sum_{i=0}^{\infty}a_i\cdot2017^i for nonnegative integers aia_i less than 20172017. Compute a0+a1a_0+a_1.
2017Discrete Math Test
2017 Geometry #6

Source:

11/19/2022
Let △ABC\triangle ABC be a right triangle with right angle ∠B\angle B. Suppose the angle bisector ll of BB divides the hypotenuse ACAC into two segments of length 3−1\sqrt{3}-1 and 3+1\sqrt{3}+1. What is the measure of the smaller angle between ll and ACAC, in radians?
2017Geometry Test
2017 Guts #6

Source:

11/25/2022
You roll three six-sided dice. If the three dice and indistinguishable, how many combinations of numbers can result?
2017Guts Round