# cubes

1. ### Finding the derivative using the definition of limit = cubes?

I must prove that the derivative of x^2/3 is 2/3x^-1/3 by using the definition but I don't know where to go after the initial plug in , that is if I even did it right. lim ((x+h)^2/3-(x)^2/3)/h h->0
2. ### Number Theory-- Sum of Cubes

Let k be a prime integer such that 100 < k < 225. How many distinct values of k exist such that k = a^{3} + b^{3} where a and b are both positive integers? The answer key says 0 and I suspect this has something to do with k being prime. What's the explanation behind this?
3. ### How many Rubik's Cubes = the universe...?

Dear forum members, Firstly, I am new to this forum and a complete non-math person, so please forgive me if I posted in the wrong area. I am an artist and am working on a sculpture that requires some math that is way above my paygrade (I know my 7 times tables, up to 7x7!), so I am hoping...
4. ### Applications of vectors and trigonometry to 3d cubes... Really desperate for help

Hi. So I need help with some math questions. I've asked my friends but they're kind of stuck too. 1.http://s1295.photobucket.com/user/chloe ... 5.png.html It is supposed to be a cube that is sticking out of the ground. We were given: The ground coincides with the x,y-plane and that the y-axis...
5. ### Applications of vectors and trigonometry to 3d cubes help??

Hi. So I need help with some math questions. I've asked my friends but they're kind of stuck too. 1.http://s1295.photobucket.com/user/chloe ... 5.png.html It is supposed to be a cube that is sticking out of the ground. We were given: The ground coincides with the x,y-plane and that the y-axis...
6. ### Lengths in cubes.

Let ABCDA'B'C'D will cube, such as in the figure. points K, L, M, N lie on the middle of edge of the AD, BC, A'B ', C'D'. Points P and Q lie on the segments KM and LN. The edge of the cube is 2 Prove that PQ> √ 2 The tasks are edited by google translator, so sorry for linguistic confusion...
7. ### Cubes - sidelengths and ratios.

what are the side lengths of 2 different cubes that are 35cm and 42cm? what is the ratio of the volume of the smaller ot the volume of the larger in simplest from?
8. ### Cubes upon cubes

Can you name off the cubes whose base number exponents have their digits sum up to the cube of the base number? (yes undefined, this is in OEIS) Moderator edit: Approved challenge question.
9. ### Fundamental group of 1-skeleton of cubes

How do you compute the Fundamental group of the 1-skeleton of the 3-cube I^{3} = [0,1]^{3} ? What about the Fundamental group of the 1- skeleton of the 4-cube I^{4} ? I know the Fundamental group of a space X at a point x_{0} is the set of homotopy classes of loops of X based at x_{0} . And...
10. ### Sum of cubes.

\begin{array}{l} prove\;that\; \\ \\ 1^3 + 2^3 + 3^3 + ............ + 100^3 = (\frac{{100 \times 101}}{2})^2 \\ \\ \end{array}
11. ### Cubes perspective problem

Hello! I would like to know how to calculate perspective precedence in 3D space. (I'm not a mathematician, so I don't know if it's the correct term, but I will try to explain what I need). I have an observer in space (px, py, pz). I also have a Rubik’s Cube, with 27 "little cubes". I have to...
12. ### red and black cubes

I've got a maths exam next week and i need to know how to work this question out for my revision so please could u show me: There are some cubes in a bag. The cubes are eithert red (R) or black (B). The teacher says: If you take a cube at random out of the bag, the probability that it will be...
13. ### Cubes, networks and shortest path.

Please see the question in the image below: I would be extremely grateful to anyone who could explain this question to me step-by-step, eventually arriving at the final answer, as I have spent almost a week on it, and I still do not think I am getting anywhere at all - it is not an easy...
14. ### Adding a Rational Expression with difference of cubes.

I've been stuck on this question for about a half hour. I really don't think the answer I'm getting is correct. \frac {(x-y)^2}{x^3-y^3} + \frac {2}{x^2+xy+y^2} Is the LCD: (x-y)(x^2+xy+y^2)? I feel like I'm getting thrown off because I'm so use to factoring trinomials when finding the LCD...
15. ### Sum of Two cubes

Hi I am having a few problems with a couple of questions of an algebra revision assignment. I have never heard of, nor been taught how to do the sum of two cubes up until this point. a) 54x^3 +2 b) x^6 -7x^3 -8 I have been having a go with the first one as it seems simpler. Using the theory I...