MathDB

6

Part of 2016 ASDAN Math Tournament

Problems(6)

2016 Algebra #6

Source:

8/6/2022
Compute all real solutions (x,y)(x,y) with x≥yx\geq y that satisfy the pair of equations \begin{align*} xy&=5\\ \frac{x^2+y^2}{x+y}&=3. \end{align*}
2016Algebra Test
2016 Calculus #6

Source:

8/8/2022
For what positive value kk does the equation ln⁡x=kx2\ln x=kx^2 have exactly one solution?
2016Calculus Test
2016 Discrete #6

Source:

8/10/2022
A container is filled with a total of 5151 red and white balls and has at least 11 red ball and 11 white ball. The probability of picking up 33 red balls and 11 white ball, without replacement, is equivalent to the probability of picking up 11 red ball and 22 white balls, without replacement. Compute the original number of red balls in the container.
2016Discrete Math Test
2016 Guts #6

Source:

8/14/2022
Suppose we have 33 baskets and 44 distinguishable balls. Each ball is placed into a randomly selected basket. Compute the probability that the basket with the most balls has at least 33 balls.
2016Guts Round
2016 Geometry #6

Source:

8/11/2022
In the diagram below, square ABCDABCD has side length 44. Two congruent square EGIKEGIK and FHJLFHJL are drawn such that AE=FB=BG=HC=CI=JD=DK=LA=1AE=FB=BG=HC=CI=JD=DK=LA=1 and EF=GH=IJ=KL=2EF=GH=IJ=KL=2. Compute the area of the region that lies in both EGIKEGIK and FHJLFHJL.
2016Geometry Test
2016 Team #6

Source:

8/17/2022
Rectangle ABCDABCD has AB=20AB=20 and BC=15BC=15. 22 circles with diameters ABAB and ACAC intersect again at point EE. What is the length of DEDE?
2016team test