User contributions for Xpmath

19:1119:11, 20 November 2009 diff hist −448 User:Xpmath Undo revision 32960 by Thunder365 (Talk) current

11:1511:15, 16 July 2009 diff hist −86 User:Xpmath →Goals for 9th grade
10:4510:45, 16 July 2009 diff hist +397 N 1965 IMO Problems/Problem 6 Created page with '== Problem == In a plane a set of <math>n</math> points (<math>n\geq 3</math>) is given. Each pair of points is connected by a segment. Let <math>d</math> be the length of the lo…'
10:4410:44, 16 July 2009 diff hist +537 N 1965 IMO Problems/Problem 5 Created page with '== Problem == Consider <math>\triangle OAB</math> with acute angle <math>AOB</math>. Through a point <math>M \neq O</math> perpendiculars are drawn to <math>OA</math> and <math>O…'
10:4410:44, 16 July 2009 diff hist +240 N 1965 IMO Problems/Problem 4 Created page with '== Problem == Find all sets of four real numbers <math>x_1</math>, <math>x_2</math>, <math>x_3</math>, <math>x_4</math> such that the sum of any one and the product of the other …'
10:4310:43, 16 July 2009 diff hist +668 N 1965 IMO Problems/Problem 3 Created page with '== Problem == Given the tetrahedron <math>ABCD</math> whose edges <math>AB</math> and <math>CD</math> have lengths <math>a</math> and <math>b</math> respectively. The distance be…'
10:4310:43, 16 July 2009 diff hist +635 N 1965 IMO Problems/Problem 2 Created page with '== Problem == Consider the system of equations <cmath>a_{11}x_1 + a_{12}x_2 + a_{13}x_3 = 0</cmath> <cmath>a_{21}x_1 + a_{22}x_2 + a_{23}x_3 = 0</cmath> <cmath>a_{31}x_1 + a_{32}…'
10:4210:42, 16 July 2009 diff hist −1 1965 IMO Problems/Problem 1 No edit summary
10:4110:41, 16 July 2009 diff hist +250 N 1965 IMO Problems/Problem 1 Created page with '== Problem == Determine all values <math>x</math> in the interval <math>0\leq x\leq 2\pi </math> which satisfy the inequality <cmath>2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{…'
10:4010:40, 16 July 2009 diff hist +1 1964 IMO Problems/Problem 6 →Problem
10:3910:39, 16 July 2009 diff hist +13 1964 IMO Problems/Problem 6 →Solution
10:3910:39, 16 July 2009 diff hist +13 1964 IMO Problems/Problem 5 →Solution
10:3810:38, 16 July 2009 diff hist +13 1964 IMO Problems/Problem 4 →Solution
10:3810:38, 16 July 2009 diff hist +13 1964 IMO Problems/Problem 3 →Solution
10:3710:37, 16 July 2009 diff hist +13 1964 IMO Problems/Problem 2 →Solution

18:3618:36, 15 July 2009 diff hist +597 N 1964 IMO Problems/Problem 6 Created page with '== Problem == In tetrahedron <math>ABCD</math>, vertex <math>D</math> is connected with <math>D_0</math>, the centrod of <math>\triangle ABC</math>. Lines parallel to <math>DD_0<…'
18:3518:35, 15 July 2009 diff hist +338 N 1964 IMO Problems/Problem 5 Created page with '== Problem == Suppose five points in a plane are situated so that no two of the straight lines joining them are parallel, perpendicular, or coincident. From each point perpendicu…'
18:3418:34, 15 July 2009 diff hist +326 N 1964 IMO Problems/Problem 4 Created page with '== Problem == Seventeen people correspond by mail with one another - each one with all the rest. In their letters only three different topics are discussed. Each pair of correspo…'
18:3418:34, 15 July 2009 diff hist +407 N 1964 IMO Problems/Problem 3 Created page with '== Problem == A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Eac…'
18:3318:33, 15 July 2009 diff hist +158 N 1964 IMO Problems/Problem 2 Created page with '== Problem == Suppose <math>a, b, c</math> are the sides of a triangle. Prove that <cmath>a^2(b+c-a)+b^2(c+a-b)+c^2(a+b-c)\le{3abc}.</cmath> == Solution =='
18:3118:31, 15 July 2009 diff hist +6 1964 IMO Problems Undo revision 32320 by Xpmath (Talk)
18:3118:31, 15 July 2009 diff hist +6 1964 IMO Problems Undo revision 32321 by Xpmath (Talk)
18:3018:30, 15 July 2009 diff hist −6 1964 IMO Problems →Day II
18:2918:29, 15 July 2009 diff hist −6 1964 IMO Problems →Day I
18:2918:29, 15 July 2009 diff hist +476 1964 IMO Problems/Problem 1 →Solution
18:1618:16, 15 July 2009 diff hist +257 N 1964 IMO Problems/Problem 1 Created page with '== Problem == (a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math>. (b) Prove that there is no positive integer <math>n</mat…'
18:1318:13, 15 July 2009 diff hist +2,507 N 1964 IMO Problems Created page with 'Problems of the 6th IMO 1964 in USSR. == Day I == === Problem 1 === (a) Find all positive integers <math>n</math> for which <math>2^n-1</math> is divisible by <math>7</math…'