unique

1. Smallest interval for existence of unique solution of differential equation

The smallest interval on which a unique solution exist for the IVP yâ€²=e^(2y), y(0)=0, is what? A)|x|<=1/2e B)|x|<=2e C)|x|<=2/e D)|x|<=1/e I am confused which one is correct. Please help.:confused:
2. Unique combinations of set

Letâ€™s say i have set with the elements { 1,2,3,4,5,6,7,8,9,10,11,12,13,14}. Is there a formula how I can calculate how many unique combinations (the order of the elements are not relevant) there are possible. And this combination can be of every length (can have a length of 1, but also...
3. Unique Sums

I have a problem that has been on my mind for years but I have not been smart enough or patient enough to think it through.:spin: I want a set of numbers such that any subset of numbers chosen and then successively added or subtracted from a running total would be decipherable solely from the...
4. The unique multiplicative inverse

How can prove that the multiplicative inverse is unqiue?
5. Unique Circle Area problem

I have a roll (circle) that contains widgets (pins/lugs). I know dimensions about this roll of widgets and I'd like to estimate when I have 5000, 3000, 2000, and 1000 widgets left on the roll. Here is how I set up the problem to solve: If I know how many widgets I have to start (W) and I know...
6. Help with Solving a System of Equations with a Unique Solution

I'm a bit confused by the Echelon Method. The directions in my example say to solve a system of equations with a unique solution. From the reading I gather that a unique solution is one in which the line of two graphs intersect at one point. The two equations listed are: 3x + 10y = 115 11x...
7. Unique digital fractions sum to one

What equation ab/cd+efg/hij=1 is unique since it expresses "1" as sum of two fractions using all the digits from 0 to 9 exactly once each. Hint: both addends equal 1/2.
8. Unique Platonic solids' part

For the five Platonic solids (regular polyhedra), find which number among all their corners, edges and faces is unique.
9. Decimal representation is unique

.99..... and 1.00..... to n decimal places are not the same no matter what n is, but their difference approaches zero as n approaches infinity, just as the difference between any two n-place decimals in consecutive order does as n approaches infinity.
10. Overlapping clouds of points: maximize unique intersection, minimize points count

Hello guys. I'm facing a problem at work, and would like to know if maybe there is ready information about some part of the following problem. Maybe you guys can give me a keyword so i can find more information, or hopefully a scientific article. Here is the problem: Setup The matrices...
11. How to EXPLAIN? Arithmetic Progression unique digit value

Given the formula y(y+1) for all positive integer including 0 , why the digit value will never end up in 4 or 8? i tried brute force and notice that 0x1=0-------------+0 1x2=2-------------+2 2x3=6-------------+4 3x4=12------------+6 4x5=20------------+8 5x6=30------------+10...
12. Unique Sums

(I've studied maths in French so forgive me if my language is off sometimes) I'm trying to find a formula that gives all unique numbers you can get out of imputed numbers. For example if I imput 6,7 and 8 I will get: 6 - 7 - 8 - 6+7 - 6+8 - 7+8 - 6+7+8 - 6+7k - 7+6k - 8+6k - 6+8k - 7+8k -...
13. Reduced Row Echelon Form is Unique Proof

Let R1 and R2 be reduced row echelon forms of A. Then R1<->R2 by elementary row operations. Therefore: R1 and R2 have same number of non-zero rows, same location of the (0,..0,1,0,..0)columns, and same elements in the non-zero rows. Examples \begin{vmatrix} 1 &0 & 2 &1 \\ 0 & 1&3...
14. Reduced Row Echelon Form is Unique Proof

No column in RREF containing a 1 and the rest zeroes can be changed by Elementary Row Operations without violating RREF.
15. Is a complete factorization unique?

Say we are asked to factor a polynomial completely over the integers Is there more than one possible result? for example (3x+3) factors completely as 3(x+1) but if I give as an answer (-3)(-1)(x+1), is it wrong?
16. Show there exists a unique solution

y' = 1/(2y*sqrt(1-x^2)) Without solving the initial-value problem, argue that there exists a unique solution. I can solve it and all, but the existence and uniqueness kind of confuse me. I think it's along the lines of F(x,y) = 1/(2y*sqrt(1-x^2)) y=! 0, x =! +-1 Fy(x,y) = -1/(2y^2 *...
17. My kind of unique intro I guess

Hello I have joined this forum to help seek answers in math. I don't know if anyone else is like this, but I am currently at Calculus 1, but the thing is my "math mind" seems to go beyond this. As in, I can think of complex math ideas and when I ask my college math profs these questions, most of...
18. Is the charge distribution for an electric field unique?

If the electric field and boundary conditions are known exactly for a region of space, is it true that there exists only one charge distribution in that region of space that could have produced it? My understanding of the uniqueness theorem in electrostatics is that for a given charge...
19. Show that there exists a unique mapping $g:B \rightarrow A$, such that $gof=i_A$ and

please,check my answer to the folowing problem: "Let $i_A:A\rightarrow A$ and $i_B:B \rightarrow B$ be two identity mappings and let $f:A \rightarrow B$ be a bijection. Show that there exists a unique mapping $g:B \rightarrow A$, such that $gof=i_A$ and $fog=i_B$". my solution: (1) $f$...
20. Unique Integer Mapping with Phi and the Golden Angle

One of the most interesting properties of the golden ratio is it's supreme irrationality above all others. Of course, the golden angle is essentially nothing more than a restatement of phi so the same holds true for it as well. Now it may not seem from the outset that this property could...