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1. Question About the Photoelectric Effect for Lower Frequencies

I'm going over the photoelectric effect and have run into a conceptual problem, and was hoping for some help in resolving it. In particular, I am looking at the frequencies below the threshold frequency of whatever metal is being examined. So, because of the lower frequency, there will be no...
2. Coordinates of a particle (coupled differential equations)

Wow, interesting. So \dot{z}=iωz → \dot{z}-iωz=0 because iz=ix-y. Thank you! Sorry, one more question. Now that I have that, when solving it I get z=z_{0}e^{ωt}, but the answer has an additional phase angle \phi in it, so I was just wondering if there was a quick explanation for that. It's...
3. Coordinates of a particle (coupled differential equations)

Yes. I then get \dot{z}=-ωy+iωx=ω(-y+ix). So I can sort of see the relation here now, except my variables seem to be the wrong way, and I have no idea where the \dot{z}-iωz=o comes from still, because i would be gone if the variables were the proper way and I subbed in z for the x-iy.
4. Coordinates of a particle (coupled differential equations)

Hi. I'm not really sure what to do. As far as I know, taking \dot{z}=\dot{x}+i\dot{y}, and \dot{y}=ωx and \dot{x}=-ωy, which doesn't seem to get me anywhere. I have no idea what I am doing.
5. Coordinates of a particle (coupled differential equations)

Homework Statement I'm given two equations for coordinates of a certain particle in the xy plane, \dot{x}+ωy=0 and \dot{y}-ωx=0. Then using the complex variable z=x+iy, find the differential for z, and solve it. Hence give x and y as functions of time. Homework Equations The...
6. Vector Spaces

Homework Statement I'm trying to define a vector space over Q. Does this make any sense? Homework Equations The properties of a vector space The Attempt at a Solution Let V=Q^2 over Q. It seems to me that everything would be defined and I shouldn't be able to do anything to a...
7. Double integral, symmetry

Yes, that is it. I will make sure to do that. Thank you very much!
8. Double integral, symmetry

Homework Statement Let D be the triangular domain given by 0\leq y \leq3, (y/3)-1 \leq 1-(y/3). Then \int\int (e-x^{5}e^(sqrt(1+y^2)) Homework Equations The Attempt at a Solution There is a quick way to solve it by breaking apart the double integral and then, apparently the x^5...
9. Sequences, induction help

Thank you both very much! Those two posts cleared up my problems with it. I was thinking of it in an accumulating way :uhh: (I have no idea why, series and sequence mix up I guess :blushing:), so now it makes sense. :cool: Thanks again!
10. Sequences, induction help

Sorry, I wasn't clear enough. I'm just not seeing how it shows that. I've memorized it and am not really worried about getting it wrong, but it's really not helpful if I don't understand that it keeps under the limit. I guess my induction skills are lacking. Ok, so if ak < 3, then ak+1 =...
11. Sequences, induction help

Homework Statement Let a_n be defined recursively by a_{1}=1, a_{n+1}=sqrt(6+a_{n}) (n=1,2,3,...). Show that lim n->infinity a_{n} exists and find its value The Attempt at a Solution Observe that a_{2}=\sqrt{6+1}=\sqrt{7} > a_{1}. If a_{k+1} > a_{k}, then a_{k+2} = \sqrt{6+a_{k+1}} >...
12. Variation of Parameters, system of equations

Perhaps I'm going about this completely wrong then. How would I start out solving y''+25y=cot(5x). (I should be more specfic, when I say solve, I mean to find A solution, so y_h and y_p. I'm just not sure about how to find the y_p=u1(y_1)+u2(y_2))
13. Variation of Parameters, system of equations

Homework Statement y''+25y=cot(5x) Find one possible solution The Attempt at a Solution I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed). Ok, so I take...
14. Undetermined Coefficients, more than one term on RHS

Awesome. That sounds like exactly what I needed to know. Thanks!
15. Undetermined Coefficients, more than one term on RHS

Homework Statement y''-49y=7cos(7x)+7+e^(7x) The Attempt at a Solution I have no idea how to solve this Differential equation. I could solve one that has y''-49y=one term, but I'm stumped with more than one. First, I get the homogeneous equation, y''-49y=0 and fine y_c, then use the...
16. First Order Homogeneous Equations

Thank you, that was exactly what I needed!
17. First Order Homogeneous Equations

Homework Statement \frac{dy}{dx} = \frac{3xy}{3x^2+7y^2}, y(1)=1 Express it in the form F(x,y)=0 The Attempt at a Solution I'm not sure where I'm going wrong. I let v=y/x, v+x\frac{dv}{dx} = \frac{3x^2v}{3x^2+7x^2v^2}=\frac{x^2(3v)}{x^2(3+7v^2)}= \frac{3v}{3+7v^2} \Rightarrow...
18. Convergent or Divergent Integral: Comparison Theorem

Ok, thanks. I'm still unsure if I did the question properly. I know the answer is right, but I'm just not sure whether the work is right or not.
19. Convergent or Divergent Integral: Comparison Theorem

Sorry, I couldn't get the script right. Its \int \frac{dx}{\sqrt{x^2 - 7}} from 8 to infinity
20. Convergent or Divergent Integral: Comparison Theorem

Homework Statement Determine if the following is improper and convergent, improper and divergent, or proper \int \frac{dx}{\sqrt{x^2 - 7}} from 8 to infinity The Attempt at a Solution Since I don't know how to...
21. Question regarding integrating (int(1/u))

Homework Statement I'm confused about integrating something like \int\frac{1}{u} Sometimes the answer seems to be ln|u| and sometimes just ln(u), and I wasn't sure why it is different from problem to problem. (after subbing u back in; I'm using the u-sub method) It looks like the answer should...
22. Related Rates (I think?)

Ok, so \frac{ds}{dh} = \frac{10}{4-h} + \frac{10h}{(4-h)^2}, when the height, h, is 3, is equal to 40. So, then \frac{dh}{dt} * 40, and solving the dh/dt for 1m/hr, makes the shadow have an increase of 40 m/hr at h=3. Hopefully I'm starting to get it.
23. Related Rates (I think?)

Hmm, I am stumped. I'm not seeing how to do it at all.
24. Related Rates (I think?)

Sorry, I'm not quite sure what I'm doing. I got the 3 for the height from the question, asking the shadows rate of increase at 3. It's a one variable calculus course, so I was avoiding t to keep it down to one variable, I'm not sure at all how to do differentiation with two variables. I could...
25. Related Rates (I think?)

Interesting. So, \frac{ds}{dh} = \frac{10}{4-h} + \frac{10h}{(4-h)^2} where h is 3, the shadows rate is increasing at 40.... metres every 3 hours? That has to be wrong, since it doesn't really make any sense to me. I'm unsure of what the units would be. And, when it approaches 4, the...
26. Related Rates (I think?)

I think I understand what you mean (for a single variable course). And if I have 3 variables, that is one too many. So, since h is variable, then 1 must be variable t, and I can state it as 4-h. So, \frac{4-h}{10} = \frac{h}{s}, so s=\frac{10h}{4-h}, and s'(h)=\frac{10}{4-h} +...
27. Related Rates (I think?)

Ok, so taking that into account, I have \frac{1}{10} = \frac{h}{s}, which then can be solved to become s=10h. s'=10, so the rate at which the length s is increasing is 10 metres per hour. I'm still not sure where the stalk growth of 1 metre per hour comes in at then.
28. Related Rates (I think?)

Thanks, I'm studying for a final, and on the finals from prior years there seems to be questions like this one asked. So, after drawing the other line, I can see two triangles in the diagram. I know the details of the one triangle, so if I remember correctly, I can find the details of the other...
29. Related Rates (I think?)

Homework Statement A magic stalk starts growing at a spot 10 metres from a 4 metre lamppost. The stalk grows 1 metre per hour. Find the rate at which the length 's' of the stalk's shadow is increasing at the instant when the height h of the stalk is 3 metres. The Attempt at a Solution...
30. Transformations, Algebra Trouble

Interesting. Let me see if I understand. x(y)-2y=1-2x <----Am I to factor(not sure if that's the proper word) the left side to get that final answer then, similar to what you showed? And then I get y(x-2) after the factor Which then is y(x-2)=1-2x And then I can get my final answer of...