MathDB

7

Part of 2017 ASDAN Math Tournament

Problems(5)

2017 Algebra #7

Source:

8/20/2022
For real numbers x,yx,y satisfying x2+y2−4x−2y+4=0x^2+y^2-4x-2y+4=0, what is the greatest value of 16cos⁡2x2+y2+24sin⁡x2+y2?16\cos^2\sqrt{x^2+y^2}+24\sin\sqrt{x^2+y^2}?
2017Algebra Test
2017 Calculus #7

Source:

9/17/2022
Compute lim⁡t→0∫0tx2+4x+4t2−x2dx.\lim_{t\rightarrow0}\int_0^t\frac{x^2+4x+4}{\sqrt{t^2-x^2}}dx.
2017Calculus Test
2017 Discrete #7

Source:

10/12/2022
Alice and Bob play a game where on each turn, Alice rolls a die and Bob flips a coin. Bob wins the game if he flips 33 heads before Alice rolls a 66. What is the probability that Bob wins? Note that Bob does not in if he flips his third head the same turn Alice rolls her first 66.
2017Discrete Math Test
2017 Geometry #7

Source:

11/19/2022
Three identical circles are packed into a unit square. Each of the three circles are tangent to each other and tangent to at least one side of the square. If rr is the maximum possible radius of the circle, what is (2−1r)2(2-\tfrac{1}{r})^2?
2017Geometry Test
2017 Guts #7

Source:

11/25/2022
Point CC is chosen on the arc of a semicircle with diameter ABAB. The two circles with diameters of ACAC and BCBC intersect again at point DD. If DA=20DA=20 and DB=16DB=16, compute the length of DCDC.
2017Guts Round