1. A

    Solution to the Continuum Hypothesis

    I believe that I have solved the 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. S

    Smallest interval for existence of unique solution of differential equation

    The smallest interval on which a unique solution exist for the IVP y′=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. D

    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. I

    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. G

    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. P

    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. I

    Solve DE

    \frac{y}{y’}=\frac{xy’+(y’)^2 }{xy’’+(y’’)^2 }.
  8. G

    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. A

    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. M

    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. I

    PDE solution explanation

    Given equation : z’_{x} a(x) +z’_{y} b(y)=c . Why the solution is found by dx/a(x)=dy/b(x)= c/dz ?
  12. S

    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:
  13. D

    Solution to the problems in Probability and Statistics

    Hi, Could you please help me with these problems?:unsure:
  14. W

    True statement describing the solution of the system

    Hi there, Could anyone please explain how to solve this question? Thanks:)
  15. E

    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. P

    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. B

    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. P

    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 progressing… 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. A

    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. S

    Big-O solution - Algorithms

    Question: By using Definition of Big-O show that: Solution: Have i done this correct? Let me know