Recent content by boneill3

Homework Statement Solve y''+4y'+5y=0 find solutions for y(0)=1 and y'(0)=0 Homework Equations Quadratic equation The Attempt at a Solution Hows this look ? assume solution is in the form of y=ce^{rx} substitute y=ce^{rx} into the equation...

The integrating factor is e^{\int{\frac{2}{x}dx} = x^2 We than use this and multiply both sides by x^2 which gives x^2y'+2xy = 3 or yx^2= 3x+C divide both sides by x^2 y = \frac{3}{x}+\frac{C}{x^2}

But isn't the justification that if K >0 and K\phi(x, y) is a metric that's non negative That it can't be > \frac{K\phi(x, z)}{1+K\phi(x, z)} + \frac{K\phi(z, y)}{1+K\phi(z, y)}? You've got that the denominator = at least 1. So if x = z the function is 0.

Homework Statement Assuming the maximum electric field sustained by dry air in a cloud is 3x10^6 Vm^-1 And a distanceof 1000 meters between Earth and cloud. The cloud is 4km long and 1 km wide. ausume uniform eletric field. Find the potential difference. Homework Equations V=Ed \mu =...

Sorry I'm getting lost here. Do I need to somehow get \phi(x, y) out of the denominator?

I appreciate all your help guys.

Thanks for your help guys. In my textbook is says that the quotient topology is the finest. However in my tutorials when ever they talked about quotient topologies they always mentioned something about an equivalence relation. I think this question was meant to make me think about it which I...

It suppose to be show (X,\theta) is a mertic

I hope this clears it up. Sorry I'm not to good at latex. Let(X,\phi)be a metric space. Take K > 0 and define. \theta : X \cross X \rightarrow \real_{0}^{+},(x,y)\rightarrow\frac{K\phi(x,y)}{1+K\phi(x,y)} show that (X,\theta)is a metric so the triangle inequality \theta(x,y)...

Yeah your right it is a typo the metric space should be (X,\phi) so triangle inequality is \phi(x,y) \leq \frac{K\phi(x,)}{1+K\phi(x,y)} \leq \mid \frac{K\phi(x,z)}{1+K\phi(x,z)}\mid + \mid \frac{K\phi(z,y)}{1+K\phi(z,y)}\mid = \mid \frac{K\phi(x,z)}{1+K\phi(x,z)} +...

Thanks mate your a ledgend FIrst I calculated Q= CV to be 195 µF * 125v = 24.3 mC Q = IT solve for t = Q/I t = 6.55 seconds

Homework Statement In a camera flash unit, a capacitor is charged up over a period of several seconds (from a battery). The capacitor is discharged very rapidly -- in about 1 millisecond -- into a gas tube producing a very brief, bright flash of light. How long will it take to charge a 195...

Hi guy's I know this is more of a homework question, I posted a similar thread earlier on but I think I ended up confusing myself. I need to show that a function is continuous between metric spaces. I'll post the question and what I've done any tips on moving forward would be great. I...

Does this look alright ? I've tried to use Open balls of radius \delta and \psi So I have three metric spaces (X,\rho) (X,\bar\rho) and (Y, \theta) and a function f : X \rightarrow Y which is continuous wrt (X,\rho) So given f : X \rightarrow Y continous wrt \rho...

Thanks for your help. I have also got to prove the following Let (Y, \theta) be a metric space. Prove the following. f : X \rightarrow Y is continuous with respect to \bar\rho if and only if it is continuous with respect to \rho I know I have to show that the inverse of Open sets in...