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Hi everyone. Here's my question: How many 1 inch diameter circles would fit into a 9 inch diameter circle? This isn't for homework or anything like that. I'm just trying to figure out how many circular tartlet cups would fit into a bamboo steamer (I need to know because I'm gonna purchase some...

Hi everyone. I apologize if this question is a bit left field but I'm getting a bit desperate and I need help. Basically, I have some irregularly spaced financial data. Specifically, I've got stock price data by the second but it isn't in regularly spaced intervals. I was wondering if you folks...

Hi everyone. First off I want to apologize if this question is inappropriate in this forum because it relates to a math program/software. I just don't know where to ask this question so I hope you can help me out. Basically, I just want ask those familiar with the math program called Maple...

Hi everyone. I've got a question about implicit funvtions. say I've got this equation : m = - [ U'(C) ] / [ Z'(C) ] From this, C can be represented as an implicit function of m . But how can this be done? I mean, if I wanted to write C in terms of m, how would it look like? Any help on this...

Hi everyone. I'm having trouble solving this 2nd order DE: x"(t) + 4x'(t) - 5x(t) = 9 If there was a 0 instead of the 9, then I could solve it cuz it's just a homogeneous equation. But in this case, it's something other than 0. I've looked at some texts and websites on non-homogeneous...

Hi folks. Is anyone familiar with optimal control problems? How do you solve an optimal control problem that has a salvage term? Like for example, max int F(t,X(t),U(t)) dt + S(X(t1)) subject to X'(t) = g(t,x,u) X(t0) = Xt0 Will the Hamiltonian be different from one from a normal...

Hi everyone. I've done a differential equation problem but am unsure if I'm right. I would appreciate it if someone could look over what I did ... ------------------------------------------------------------------------------- Find x(t) for: . . .[x(t)]^2 - 2[x'(t)]^2 = c ...where c is some...

Hi folks. I have this problem: int -2x(1)*e^x(t) dt, where x(1) is x(t) when t=1 Apparently, the answer is [-2x(1)*e^x(t)] / x , but I'm not sure how it came to that. I'd appreciate it if someone explains the integration process in this problem to me. Thanks.

Hi everyone. I just wanted to ask if this integral can actually be found even without the function being explicitly shown: int [ [e^(at)] Q(t) ] dt where 'a' is a constant Is there a general form to this integral or does Q(t) actually have to be explicitly written out in order to get the...

Hi everyone. This is an extension of a problem I asked in the Differential Equation forum but I think it's more appropriate here. I'm having trouble with this integral: integral e^x(t) dt I've tried substitution and integration by parts but get stuck in both. Grrrrrrr!! Any help would be much...

Hi everyone. I'm having quite some problems with this differential equation: y'(t) + y(t) * x'(t) = -2x(1) where x(1) is x(t) where t=1 I'd like to integrate to get y(t). I've tried doing it using an integrating factor but I inevitably get stuck. Any help would be greatly appreciated. Thanks!

Hi all. I'm really having problems figuring out just how to integrate this equation: x'(t) * ln[ x'(t) ] = 1/2 * c where c is just some constant. I thought of using an an integrating factor but the equation doesn't seem to fit the form needed to do so. If anyone can help me out I would...

Hi again everyone. I have a solution to this problem but I'm not really sure if it's correct. The problem is: The position of a fly at time t is given (x, y, z) = (t, t^2, 1+t^2). A light shines down on the fly from the point (0, 0, 3) and casts a shadow on the xy-plane. What is the position...

Hi everyone. I'm having problems figuring out how to solve this problem. I don't really know where to start. It goes ... Find a parametric equation for the curve of intersection of two surfaces z = x^2 - 2y and z = 2x^2 + y^2 . If anyone can help me on this it'd be much appreciated. Thanks!

Hello. Does anyone know what the rule is to find the derivative of x^x? Or (x+1)^x?

Hello again everyone. I'm stuck with this integral problem: int [sqrt(x)] / (2x^2+1) I've tried letting u = x^2 but it's not working out too well. If someone could point me to the right direction it's be much appreciated. Thanks!

Hi everyone. I'm really having problems figuring out how to get this integral with trig substitution: intgral sign 1 / (2x^2+1) dx . I know how to get the integral if the denominator didn't have a 2 attached to the x^2, but I'm having problems with the one above. Can someone please show me...

Hi everyone. I'm having some problems with this question: Find the Taylor series centered at Pi/4 for f(x) = sinxcosx What I've done is find derivatives from orders 1 and up and evaluating them with x = Pi/4. I then used these on the general Taylor series formula to get an indication of how...

Hi everyone. I've been having trouble integrating the following function: 1 / [ 5^x + 5x] I'm not sure how integration by parts or by trig substitution would work on this. If anyone could steer me in the right direction it would be much appreciated. Thanks!

Hi everyone. I'm kinda stuck on how to find the limit of this sequence as n approaches infinity: a = [sqrt(4n^2 + 3)] / [(n - sqrt(n)] I'm not really sure how to begin. If someone can point me in the right direction it would greatly be appreciated. thanks!