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Reasonably hard infinite sum of integrals?
Σ_1^∞ (1/n)*∫_{2πn}^∞ (sin z/ z) dz = ?
Sum from n=1 to n=∞ of (1/n) times integral from z=2πn to z=∞ of sin z/ z.
5 AnswersMathematics1 decade agoy(0)=y(1)=0 and 0<d<1. Can one always find x1 and x2 such as x1-x2=d and y(x1)=y(x2)?
y denotes an arbitrary continuous curve in the plane (x,y) connecting points x=0, y=0 and x=1, y=0.
This problem has been partially solved in
http://answers.yahoo.com/question/index;_ylt=AvH5E...
It has been shown that
(1) the answer is positive for d=1/n, n=2,3 ...;
(2) for some values of d the answer is negative.
Are there other values of d, except for d=1/n, for which the answer is positive?
4 AnswersMathematics1 decade agoIs it always possible to find two points on a curve?
Points X and Y are connected by a continuous curve. We are looking for two points A and B lying on this curve that satisfy two conditions:
(1) The distance between A and B is one third of the distance between X and Y.
(2) The straight line connecting A and B is parallel to the straight line connecting X and Y.
Is it always (i.e. for any continuous curve) possible to find such points A and B?
9 AnswersMathematics1 decade agoHow to best approximate one by the sum of five Egyptian fractions II?
Find 5 integers
1 < n1 < n2 < n3 < n4 < n5 so that
Σ = 1/n1 + 1/n2 + 1/n3 + 1/n4 + 1/n5 < 1
and Σ is as close to 1 as possible.
The condition Σ < 1 was missing in the first version of this question
4 AnswersMathematics1 decade agoHow to best approximate one by the sum of five Egyptian fractions?
Find 5 integers n1, n2, n3, n4, n5 (all greater than 1) so that the sum
1/n1 + 1/n2 + 1/n3 + 1/n4 + 1/n5
is as close to 1 as possible.
2 AnswersMathematics1 decade agoWhat is the chance to kill odd number of birds with n stones, if one cannot kill several birds with one stone?
Stones are thrown one by one, and the chance to kill one bird with one stone is p.
Solution for the limiting case p=1/n -> 0 is here
3 AnswersMathematics1 decade agoWhat is the chance to get odd number of googols?
An integer between one and googol is picked randomly googol times. What is the probability that googol is chosen odd number of times.
6 AnswersMathematics1 decade agoDoes any triangle can overlap with its mirror image by more than 80%?
T is a triangle and Tm is its mirror image. One places Tm on the top of T and tries to reach the maximum overlap. Do such triangles exist that the overlapping area of T and Tm is always less than 80%?
6 AnswersMathematics1 decade agoWhat is the maximum of ba+ca+bc?
What is the maximum of ba+ca+bc, if a, b, and c satisfy the relations
a^2+ab+b^2=3 and b^2+bc+c^2=16?
3 AnswersMathematics1 decade agoIs it possible to paint the surface of a sphere in two colors in such a way ...?
that there are no equliateral triangles, whose vertices have the same color?
3 AnswersMathematics1 decade agoDo you want to get 1$?
Three players are offered a chance to get 1$. Each of them, independently of others, either rejects or accepts the offer. Rejecting the offer does not have any consequences. 1$ is given to a player randomly chosen from those players who accept the offer. A player who accepts the offer, but does not get 1$, pays the penalty of 2$.
The above procedure repeats many times. The players do not cooperate, and they do not know plans of other players.
What is the optimal strategy in this game?
8 AnswersMathematics1 decade agoCan a camel pass through the eye of a needle?
Use the model, where the camel has the shape of a regular tetrahedron with unit edges, and the eye of the needle is a circle with diameter of 0.9.
9 AnswersMathematics1 decade agoFind angles in acute triangle ABC?
Point O is the center of the circumscribed circle. Line BO intersects side AC at point D. Line CO intersects side AB at point E. ∠BDE=50 degrees. ∠CED=30 degrees.
Find angles A, B, and C.
4 AnswersMathematics1 decade agoIs there a full square in the form XX?
Can one get a full square by writing twice the same natural number X? For example, if X=123, then XX=123123, which is not a full square.
3 AnswersMathematics1 decade agoA,B,C are angles and x,y,z are sides of a triangle. Show that 60 <= (xA+yB+zC)/(x+y+z) <= 90?
Angles are in degrees
4 AnswersMathematics1 decade agoRemove your answers. It's a fraud?
http://answers.yahoo.com/my/profile;_ylt=AkDdXPoX0...
After answering one of the questions of this user I discovered that they are taken from USA Mathematical Talent Search, Round 2 Problems.
The deadline is only on 23 November, and the idea of this competition is not to ask others to solve the problems.
5 AnswersMathematics1 decade agoWhat is the minimum distance between two circles?
Squares S1 and S2 are adjacent faces of a unit cube. C1 is the incircle of S1, and C2 is the circumcircle of S2. What is the minimum distance between C1 and C2?
3 AnswersMathematics1 decade agoSolve equation x*y*z=y^2+z^2+1 for x?
x, y, z are natural numbers, and x*y*z=y^2+z^2+1. Find all values of x.
9 AnswersMathematics1 decade ago