1. O

    Combinatorics with several conditions

    Hello. I have a math problem that I need to solve, however Im really stuck and also kind of depressed now. We have 30 balls. 6 red, 7 white, 9 green and 8 blue. We want to seperate them to 4 different boxes. · First box can only contain 13 or less balls, which can be either red or...
  2. B

    Matlab Plotting Euler Iteration Against Exact Solution how to Set Initial Condition

    Hi I have the following code to plot an approximation using Euler's iteration against the exact value of the function. I have used x and y for time and population when coding the Euler iterations and t and m for time and population when plotting the exact function. I can't work out how to...
  3. X

    boundary condition

    can someone explain what dies u mean ? in the ans given , u(0, t) = 0 , and also u(10, t) = 0 ? in the lower part , i was also told that at t= 0 , u =1 , du/ dt = x i'm confused at t = 0 , u = 0 or u = 1 ???
  4. M

    Find the boundary condition of the nonlinear partial differential equations

    I have first-order nonlinear partial differential equations \frac{du}{dt}+u\frac{du}{dx} =-u^3, u\Bigr|_{t=0}=f(x) solution dt=\frac{dx}{u}=-\frac{du}{u^3} F(x-\frac{1}{u},t-\frac{1}{2u^2}) Need find boundary conditions f(x) (for example u(t=0,x)=x and find $u$) But my simple function have a...
  5. X

    condition of laplace transform

    can someone explain how to determine the condition of s ? taking 2 as an example , why the s is >5 , not >0 ?
  6. X

    form differential equation ( initial condition given)

    x(x +y ) dy/dx = y^2 , initial condition = y(1) =2 , but my ans is different...
  7. Bernhard

    Noetherian Modules - Maximal Condition - Berrick and Keating Ch. 3, page 111

    I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need someone to help me to fully understand the maximal condition for modules and its...
  8. claratanone

    First-order condition & second-order sufficient condition

    A broking firm that supplies consulting services has demand and average cost relations: P+3Q-30=0 and AC=Q+10, respectively. Your tasks is to: (a) derive the first-order condition for the firm's profit maximization; (b) verify that, at the critical point, the second-order sufficient condition...
  9. M

    Epsilon-delta condition for limits

    Greetings, I'm reading this book which does develop calculus with "infinitesimals". It's great book to learn mechanics of differentiation and integration. But proofs sometimes seem to me sketchy. I'm asking about one that puzzles and frustrates me...
  10. C

    Find all primes that satisfy the condition

    $p|2^p+1$ p is a prime I know how to prove this but I need some help in steps. In factoring $2^p+1$ we will always have a term (2+1) because we know that $a^n + b^n = (a+b)\cdot P$ where P is a polynomial... I know this is true but I don't know how to prove it But if i can prove the thing...
  11. H

    Condition Number of a square matrix

    Show that the condition number $c(\textbf{A})$ with respect to the 2-norm of a square and non singular matrix is given by $\sqrt{\rho(\textbf{A})}$ where $\rho(\textbf{A})$ is the spectral radius of $\textbf{A}$ (largest magnitude eigenvalue of $\textbf{A}^T\textbf{A}$). Is this statement...
  12. F

    Arrangement with condition

    Given n and a letter C,how many possible words of length n can be formed that are with no two consecutive C in the word. For example,if n=3,ch='b',then the word bcb,ccc,aab do not have any consecutive occurrence of 'b'.But bbc,abb,bbb have consecutive occurrence of 'b'. we can use only...
  13. J

    Finding the solution to differential equations that satisfies the initial condition.

    dP/dt=8sqrt{pt}, P(1)=6 This is my working and i prove that it does satisfy the initial condition but apparently i am still incorrect: dP/sqrt{p}=8sqrt{t}dt Integrating both sides we get: 2sqrt{p}= (16t^3/2)/3 + C Using P(1)=6: 2sqrt{6}= (16(1)^3/2)/3 + C C= 2sqrt{6} -16/3 Substituting...
  14. J

    Topological space: Condition 3

    \for A,B \in \mathfrak{T}, A \cap B \in\mathfrak{T} What is a good way to prove this true? One video I saw said it can be proved by induction but I haven't done an induction proof on a set before. I thought maybe an element proof would be easier to work out.
  15. G

    Condition for equality to hold

    Question is Are this equal? 1/(a+b) =1/a + 1/b Does this have a condition for equality?
  16. J

    if an integer divisible by 16 is a sufficient condition to be divisible by 8...

    if an integer divisible by 16 is a sufficient condition to be divisible by 8 then prove or disprove by counterexample I say it is sufficient, its a p --> q statement let n be an integer such that 16|n, then 16k=n for some integer k by definition n must be even and k may be even or odd then...
  17. J

    condition for differentiability

    I have to determine if f(x,y) = \frac{x}{y} + \frac{y}{x} is differentiable at all points in its domain and of class C^1 \frac{\partial f}{\partial x} = \frac{1}{y} - \frac{y}{x^2} \frac{\partial f}{\partial y} = \frac{1}{x} - \frac{x}{y^2} seems that if (x,y)=(0,0) then its not continuous or...
  18. S

    Stationary path of functional, possible Transversality condition?

    Hi everyone, I have the following functional S[y] = \int_{0}^{v}\! \left( {\frac {\rm d}{{\rm d}x}}y \left( x \right) \right) ^{2}+ \left( y \left( x \right) \right) ^{2}\,{\rm d}x Where y(0) = 1, y(v) = v, v > 0, I then showed that the stationary path of the functional is y = cosh x + B...
  19. W

    condition expection question

    Please help me prove: If X,Y∈L1(Ω,F,P) E[X|Y]=Y a.s. , E[Y|X]=X a.s. Then X=Y a.s. I need a detail proof . thank you~!
  20. C

    Separating variables and initial condition?

    I have this question: I'm not sure why the fourth option isn't showing up but hopefully it's not needed. When I separated the variables I got 2x^2=arcsint+C and when I solved for C I got the C=8. Is this right? It gave me option two, but I'm just not sure. :/ Thanks!