MathDB

4

Part of 1983 National High School Mathematics League

Problems(2)

Two Simple Sets

Source: 1983 National High School Mathematics League, Exam One, Problem 4

2/21/2020
Define two sets: M={(x,y)∣y≥x2},N={(x,y)∣x2+(y−a)2≤1}M=\{ (x,y)|y\geq x^2\} ,N=\{ (x,y)|x^2+(y-a)^2\leq 1\}. If M∪N=NM\cup N=N, then the range value of aa is (A)a≥114(B)a=114(C)a≥1(D)0<a<1\text{(A)}a\geq 1\frac{1}{4}\qquad\text{(B)}a=1\frac{1}{4}\qquad\text{(C)}a\geq 1\qquad\text{(D)}0<a<1
Tetrahedron Problem

Source: 1983 National High School Mathematics League, Exam Two, Problem 4

2/22/2020
In a tetrahedron, lengths of six edges are 2,3,3,4,5,52,3,3,4,5,5. Find its largest volume.
geometry3D geometrytetrahedron