Math challenge Definition and 83 Threads

Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other basic level math challenge thread! RULES: a) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions will be...

Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other intermediate level math challenge thread! RULES: a) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions...

Summer is coming and brings a new intermediate math challenge! Enjoy! If you find the problems difficult to solve don't be disappointed! Just check our other basic level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no...

Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other intermediate level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions...

Summer is coming and brings a new intermediate math challenge! Enjoy! If you find the problems difficult to solve don't be disappointed! Just check our other basic level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no...

Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other intermediate level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. Solutions will...

Summer is coming and brings a new intermediate math challenge! Enjoy! If you find the problems difficult to solve don't be disappointed! Just check our other basic level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no...

Summer is coming and brings a new basic math challenge! Enjoy! For more advanced problems you can check our other intermediate level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine...

It's time for an intermediate math challenge! If you find the problems difficult to solve don't be disappointed! Just check our other basic level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored...

It's time for a basic math challenge! For more advanced problems you can check our other intermediate level math challenge thread! RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results...

Homework Statement I have a triangle with top sides of 5 mm (base is then 5*sqrt(2)). The top triangle has a line cut through it, at a height of 5/sqrt(2)/2. I want to compute the amplitude as function of position as a line sweeps into the triangle that is cut off. Requirement is A(0) = 0 and...

Submitted by: @QuantumQuest Challenge Level: High School RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common...

Homework Statement Homework Equations y-y1 = m (x-x1) ---> line equation $$ (x - a)^2 + (y-b)^2 = r^2 $$ ---> circle equationThe Attempt at a Solution I tried to draw the triangles using, (1, 3) (2, 4) and (0, b) (0, b) is the tangent point to y-axisand used those points for making...

some formula related I tried to draw the problem can anyone give me clue how to solve it?

Greg asked me to post it myself. RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common knowledge to all...

Submitted and judged by: @QuantumQuest Solution credit awarded to: @ddddd28 RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as...

Submitted and judged by: @andrewkirk Solution credit: RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common...

Submitted and judged by: @QuantumQuest Solution credit: @MAGNIBORO RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is...

Submitted and judged by: @Erland Solution Credit: @SSequence for 2a, 2B, C, D RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long...

Submitted by @Erland Solution Credit: @mfb RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common knowledge to all...

Submitted by: @QuantumQuest Credit to: @stevendaryl RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common...

Submitted by @Charles Link Solved by: @MAGNIBORO and @maline RULES: 1) In order for a solution to count, a full derivation or proof must be given. Answers with no proof will be ignored. 2) It is fine to use nontrivial results without proof as long as you cite them and as long as it is "common...

Let $x, y$ be real numbers such that $$(\sqrt{y^{2} - x\,\,}\, - x)(\sqrt{x^{2} + y\,\,}\, - y)=y.$$ Prove $x=-y$. Any suggestion would be appreciated.

Here are the total point standings as of 10:33am on 12/20/2013: mfb 9 Citan Uzuki 7 Boorglar 3 jbunniii 3 Mandelbroth 2 jk22 2 hilbert2 2 economicsnerd 2 HS-Scientist 1 D H 1 jackmell 1 verty 1 Perok 1

What is this place? This forum is for people to come together and stretch their brains on math puzzles. Each week there will be a new challenge for the forum to try. What do I get for answering challenges? We're going to try a point system. The first person to post a solution will be awarded...

HI : good to see you everybody ,I am a new comer on this board Being a math teacher ,I always trained my students with various difficult problems from now on I am going to post a sequential challenging questions for people to share most of them I know the answer and the solution of it , maybe...

Hello. I have been trying to find this limit: Lim as x --> 1 of (sin((1-x)/2)*tan(Pi*x/2)) Of course I don't want to solve it using L'Hospital. I have tried several ways but ended up in one of these. lim as y -->0 of (y*tan(pi/2-y*pi)) The answer when using L'Hospital is 1/pi...

Some of my friends, upon finding out that I'd joined these forums, decided to give me a math challenge problem they thought couldn't be solved. Does everyone get the same answer? It goes as follows: A knight jumps on a chess board (assume it makes a legal move) from point A to point B...

Homework Statement So the goal is to reach a distance H in the x-direction, starting from a height H in the y-direction, and you need to minimize the speed, and find the smalest and angle. Homework Equations i did: dx = V cos(theta) *t and y = y_0 +V sin(theta)*t-1/2*g*t^2 Vx =...

Homework Statement So I'm trying to find the integral of P = 2xyz^2 along the curve c which is defined by: x=t^2 y=2t z=t^3 t goes from 0 to 1 So the q says that it is the integral of P dr along c Homework Equations The Attempt at a Solution So I know that this...

Homework Statement Prove that the set A = {(x,y) in R2 : xy ≠ 1} is open in the metric space (R2, d), where d is the Euclidean metric. The attempt at a solution A is open if for any p in A, I can find an open ball centered at p that is contained in A. This would be easy if I could find the...

kepler's law! hi, does anybody know how to prove that the eccentricity multiplied by the directrix is equal to [itex] \frac {b^2}{a} [\itex]? i found that the eccentricity of an ellipse is equal to c/a. i also found that the directrix is equal to a/e. the way i see it, if i multiply e...

1. calculate the length of the following paths: f(t) = (7, t, t^2) over 1<t<3 the way i was taught in class to calculate the length of a curve is to integrate the magnitude of the velocity, but i can't seem to naturally integrate the magnitude of (0, 1, 2t) similarly for: f(t) =...