神马作文网美国数学竞赛题（都英语进）
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美国数学竞赛题（都英语进）
1.Make two random marks on a long stick.
(a) If you then break the stick into k pieces of equal length,what's the chance the two marks are on the same piece?
(b) If you then break the stick into k pieces of random lengths,what's the chance the two marks are on the same piece?
2.Leonhard has ten rods having lengths 1,2,...,10 respectively.How many different ways are there to make a triangle by choosing three appropriate rods?
3.A point is chosen randomly inside a square of side length 5,and a unit circle is drawn with that point as its center.Calculate the probability that the circle does not intersect either of the square's diagonals or any of its sides.
4.Circles A,B and C with radii 2,4,and 6 respectively are tangent to one another.The common external tangent to circles A and B intersects the common external tangent to circles A and C at point x.Find the measure of angle x.
5.In the complex plane,let u and v be two distinct solution of .Find the probability that .
1.Make two random marks on a long stick.
(a) If you then break the stick into k pieces of equal length,what's the chance the two marks are on the same piece?
(b) If you then break the stick into k pieces of random lengths,what's the chance the two marks are on the same piece?
2.Leonhard has ten rods having lengths 1,2,...,10 respectively.How many different ways are there to make a triangle by choosing three appropriate rods?
3.A point is chosen randomly inside a square of side length 5,and a unit circle is drawn with that point as its center.Calculate the probability that the circle does not intersect either of the square's diagonals or any of its sides.
4.Circles A,B and C with radii 2,4,and 6 respectively are tangent to one another.The common external tangent to circles A and B intersects the common external tangent to circles A and C at point x.Find the measure of angle x.
5.In the complex plane,let u and v be two distinct solution of .Find the probability that .
1,(a)这2点在任何一段是等可能的,所以一共有K^2可能情况,而在同段的情况K种,所以2点同段概率是K/K^2=1/K
(b)假长为单位1,2点距离x,那么K-1次断点都不在2点间的可能为(1-X)^(K-1)
显然2点同段可能是(1-X)^(K-1)
2,1到10,选择3个组成三角形.假使0
(b)假长为单位1,2点距离x,那么K-1次断点都不在2点间的可能为(1-X)^(K-1)
显然2点同段可能是(1-X)^(K-1)
2,1到10,选择3个组成三角形.假使0