# solution

1. ### Solution to the Continuum Hypothesis

I believe that I have solved the Continuum Hypothesis: https://en.wikipedia.org/wiki/Continuum_hypothesis Assume CH is true. Then $|\mathcal{P}(\mathbb{N})| = |\omega_1|$ and we have a way to prove that my $T$ sequence here cannot contain all of the elements of $\omega_1$ using the...
2. ### 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:
3. ### Very basic solution help.

Hello it has been a while since I have engaged mathematics formally. I am trying to determine my odds of winning a contest. I had 1/300 chance of winning, and then received 1000 entries. This gave me 1/194 chance of winning. After receiving another 200 entries, I had a 1/181 chance of...
4. ### Solution help

Let the function g be defined by g(x) = 5x + 2. if (sqrt (g (a / 2))), what is the value of a?
5. ### Explain this solution for this profit/loss problem?

By selling an article at 80% of its MP, a merchant makes a loss of 12% what will be the profit /loss percent made by the merchant if he sells the article at 95% of its M.P? Sol: 80% is equated to 88 95% is equated to 104.5 104.5 - 100 = 4.5 Why 80% is equated to 88 & 95% is equated to 104.5??
6. ### Solution of partial differential function.

Dear all, I have the following Partial Differential Function. It's a Second-order variable coefficient homogeneous linear differential equation. (A.Y')+CY=0 in which A and Y are functions of x, C is a non-zero constant. A is not an elementary function. So is it possible to represent Y in...
7. ### Solve DE

\frac{y}{yâ€™}=\frac{xyâ€™+(yâ€™)^2 }{xyâ€™â€™+(yâ€™â€™)^2 }.
8. ### Explain this shortcut C.I solution.

A sum of money placed at Compound interest becomes 27 times of itself in 15 years. In 25 years, it will becomes how many times? Shortcut Sol: 3^3 = 3*5 ?=5*5 ? = 3^5 = 243 times. Actual CI formulae is CI = P(1+\large\frac{r}{100})\normalsize^{n} But solution looks totally different. Please...
9. ### Which solution is better for this predicate?

We have this predicate: Now I have to turn this in English. I come up with three answers: 1) x is a prime number if x is greater than 1, and if for every given y that is divisible by x, then y is either 1 or x itself. 2) x is a prime number if x is greater than 1, and for every given...
10. ### Solution of the process in Bates Model

Hi all, I have to do a Monte Carlo Simulation for Stoch prices by using the Bates Model. In the Black Scholes Model I can calculate St=S0*exp((r-sigma^2/2)t+sigmaWt). My problem is that I do not know how to calculate St in Bates Model. Could anyone please help me?
11. ### PDE solution explanation

Given equation : zâ€™_{x} a(x) +zâ€™_{y} b(y)=c . Why the solution is found by dx/a(x)=dy/b(x)= c/dz ?
12. ### Number of constants in general solution

The number of arbitrary constants in the general solution of the differential equation will be 3 or 6?:confused::confused:

14. ### True statement describing the solution of the system

Hi there, Could anyone please explain how to solve this question? Thanks:)
15. ### Sorting functions asymptotically, solution correct?

The task is to sort functions f_i for i = 1, \dots, 4 defined as follows: f_1 := log(n^{3n+1}) f_2 := \sum_{i=0}^{2n} 3i f_3 := 4 \cdot {n \choose 2} f_4 := 2n^3 Ideas: f_1 = log(n^{3n+1}) = (3n + 1) \cdot log(n) = 3n \cdot log(n) + log(n) \in \Theta(n \cdot log(n)) f_2 =...
16. ### Prove general solution for deppresed cubic equation y^3+py+q=0 given a discriminant

I've been given the following problem and I can't seem to figure out the solution, would appreciate any help and direction to solution ! Let's look at the equation : y3 + py + q = 0 (*) We shall define Delta (or d in short) d = 4p3 + 27q2 Prove that : a) If d > 0 , then (*) has a...
17. ### How to Find Optimal Solution here?

Question: I found the values which make equals to 0 for first derivative. How can I find the correct values? Would you help me, please?
18. ### Matrix in relation to solution subspace

Hi guys, I am having serious trouble analysing the following question: I have been thinking about it for an hour, but I am not progressingâ€¦ Can anybody help out? Let A be a matrix over R of order 4x4, with rank 2. Suppose that the vectors u=(2,1,2,0) v=(1,-1,2,4) w=(1,0,2,-1) are...
19. ### Seeking sequence solution

It's been awhile since I've had to do anything with sequences, a very long while. I'm not even sure if I'm going to ask the question right, but I'll give it a shot. I'm wondering if there is an equation to help me figure out the nth term in the sequence. It cycles through 0 8 6 4 2 0 8 by...
20. ### Big-O solution - Algorithms

Question: By using Definition of Big-O show that: http://prntscr.com/lqdsy1 Solution: http://prntscr.com/lqdsrl Have i done this correct? Let me know