# challenge

1. ### Which side is greater? my challenge #1

Determine which side has the larger value: \sqrt{2 \ } \ + \ \sqrt{7 \ } \ + \ \sqrt{287 \ } \ \ \ versus \ \ \ 21 You are not allowed to do it by estimating roots. You may square each side when appropriate. You can subtract or add radicals and/or non-radicals from each side as...
2. ### A challenge to the theory of special relativity

I am well aware of Einstein's thought that nothing can move faster than the velocity of light. However (and this is verified experimentally), there is Cherenkov radiation. From what I've read about it, it is an entity that has a velocity greater than light in a vacuum. For this, Cherenkov...
3. ### A little challenge

Proof, using derivative, that sen(xÂ²) is not periodic.
4. ### A little challenge for you

Using Calculus one methods, proof that Sen(xÂ²) is not periodic. ( F is periodic if there T, such that f(x+t) = f(x), whatever x belonging to Df)
5. ### Inequality challenge

Given some real numbers x_1 \;,\; x_2 \;,\; x_3 \;,\; ... \;,\; x_n \; > \; -1 with x_1^3 \;+\; x_2^3 \;+\; x_3^3 \;+\; ... \;+\; x_n^3 \; = \;0 prove that x_1 \;+\; x_2 \;+\; x_3 \;+\; ... \;+\; x_n \; \leq \; \frac{n}{3}
6. ### Challenge to the theory of Scalar Fields and Heat Death

Golf and skateboarding are played on a scalar field of varying heights. Newtonian physics is played on scalar higgs fields, because all scalar fields are newtonian. http://en.wikipedia.org/wiki/Scalar_field My challenge to the theory of scalar fields is they violate Conservation Of Surface...
7. ### Challenge : Matrix power and primes

I discovered something very fun. Let us take any matrix n x n (n>1). When powering some matrix (4*4) we find that at each step of powering the matrix contains at least one prime. Can you find a matrix A (2x2 or more) with the longest sequence with at least one prime? I mean : A contains at least...
8. ### CHALLENGE: "Over the Rainbow" in math notation

**Sorry if this is in the wrong section! It didn't seem to fit anywhere and "Applies Mathematics" seemed promising I thought it would be fun to try to write "Somewhere Over the Rainbow" in math notation, and I wanted to document my struggles here. Feel free to post ideas or correct my...
9. ### Euromillions challenge

Here is my challenge for the next 10 draws : 12 numbers : 1-3-8-11-20-30-34-35-38-41-44-46 Stars : 3-4-6-7-8 I guaranty at least 4 numbers plus 2 stars. What my probabilities to succeed? Here you can check the draws : http://www.euro-millions.com/results.asp
10. ### Challenge to computing theory - log but never random access

There is no such thing as random access ever. Hashtables are said to be near (maybe log of log) random access, going directly to what you look up by a key. Arrays are said to be exactly random access. You give it a memory address and it goes straight there. But there is a log cost conveniently...
11. ### Equation Challenge

Find the "x" values of this equation: "6x^2-47x-63" Good Luck
12. ### Trig Functions + Identities 'Challenge Questions' (Homework)

So, I'm having a tough time with these two questions. I don't know how to approach them or what to do. For the first one, I tried drawing a unit circle, having the intersection of the two lines as (0,0), but the answer I got was wrong. For the 2nd question, I'm lost. All I know is that A,B,C...
13. ### Trigonometry extra challenge question

Hi, I'm completely stuck on this question and I was wondering whether anyone could offer any help ?
14. ### Math Challenge FREE - Android.

Hello Guys! For the math aficionado. Play Math Challenge and test yourself for free. Many Games. https://play.google.com/store/apps/deta ... atico_Free
15. ### Math Challenge +-*/ Android Game

How different can a Math game be? Well we believe, at TurtleLabs, that it can be very different and better. It can be different aesthetically and it can give you a new and original game play. Check out our arithmetic games —Magical Squares! — and be careful …those questions don´t just sit...
16. ### Challenge Problem

Find two points on the curve y = x^4 -2x^2 - x that have a common tangent line. Bonus: Prove that there are only two such points. I have a midterm tomorrow and I cannot solve this. Can someone solve and explain how/why they did what they did?
17. ### Challenge problem for High School Students

Suppose there are n positive integers all greater than 100, such that for all integers N\geq 1000, N can be expressible as any sum of these integers. What is the minimum value of n? As an example, take the integers 5 and 8. 10, 18, and 26 can be expressible as a sum of these integers since...
18. ### [Challenge] Hypermodern magazine

This is just for fun. Underwood Dudley wrote a book (recommended!) called Mathematical Cranks, and in one chapter he discusses a crank publication, Hypermodern, written and produced entirely by one person whom Dudley refers to only as "A. C.". One of the articles (issue 12) presents a series of...
19. ### Challenge Problem

Suppose that f(z_0) = g(z_0) = 0 and that f'(z_0) \, \neq \, 0 and g'(z_0) \, \neq \, 0 both exist. Using f'(z_0) = \lim_{z \rightarrow z_0} \frac{f(z) -f(z_0)}{z - z_0} given the theorem \lim_{z \rightarrow z_0} f(z) = w_0 and \lim_{z \rightarrow z_0} F(z) \, = \, W_0 \, \neq \...
20. ### Math Q&A challenge (Part 11)

You have an integer number where any digit appears at most twice. The sum of all neighboring four digits in this number is a square. Example: 205290 is such a number because no digit appears more than twice, and 2+0+5+2, 0+5+2+9, and 5+2+9+0 are squares. What is the maximum possible value...