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  1. N

    Calculating Triple Integrals in Mathematica

    This problem was given to me by my instructor.
  2. N

    Calculating Triple Integrals in Mathematica

    Homework Statement Evaluate ∫∫∫\sqrt{x^{2} + y^{2}} dA where R is the region bounded by the paraboloid y=x^2+z^2 and the plane y=4 Homework Equations I believe this is a problem where cylindrical coordinates would be useful 0 ≤ z ≤ \sqrt{4-x^2} 0 ≤ r ≤ 2 ( I think this is wrong). 0 ≤ θ ≤...
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    How to calculate curvature of a vector in Mathematica.

    I can't believe I overlooked that. I also removed the parentheses. Now I'm getting 26.89. Thanks for the help
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    How to calculate curvature of a vector in Mathematica.

    I tried it 3 different ways and I still get 20.39 http://i.imgur.com/mQW6TaO.png http://i.imgur.com/DmTseJc.png http://i.imgur.com/QKfTfoW.png
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    How to calculate curvature of a vector in Mathematica.

    I'm not getting a number. http://i.imgur.com/mQ4Pfac.png I'm guessing I have incorrect syntax. Edit: I realized i didn't capitalize the 'p' in Pi. now I"m getting 13k though I got 20.39
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    How to calculate curvature of a vector in Mathematica.

    From my textbook. I scanned the page I found it from. http://i.imgur.com/AivojRL.jpg
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    How to calculate curvature of a vector in Mathematica.

    Okay, thanks. I have one last question. How can I use the inte\frac{}{}rval <0,4pi> in this equation? I'm just a little confused about why this formula, k = |\frac{r(t)' X r(t)''}{r(t)'^3}| gives a different answer to the formula you posted
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    How to calculate curvature of a vector in Mathematica.

    Haha, I actually managed to plot it, but I thought it was wrong because I wasn't expecting a huge wave. I was also told to calculate the length of the curvature. Do you think this would be an acceptable answer? http://i.imgur.com/HHYzFy7.png Is there a way to simplify this expression?
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    How to calculate curvature of a vector in Mathematica.

    It doesn't seem to make a difference. http://i.imgur.com/woWlabm.png http://i.imgur.com/ptUZcVG.png
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    How to calculate curvature of a vector in Mathematica.

    Homework Statement r(t)={(4+cos20t) cost,+(4+cos20t) sint,+0.4sin20t} Calculate the curvature of r[t] for 0≤t≤4pi Homework Equations k = | r' x r'' | / | r' |^3 The Attempt at a Solution r[t_]:={4+Cos[20t]*Cos[t],4+Cos[20t]*Sin[t],0.4Sin[20t]} k[t_]:=Norm[Cross[r',r'']]/Norm[r']^3...
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    Using Node-Voltage method in the phasor domain

    I was wondering if there is an easier way to solve circuits using matrix inversion if I have complex numbers. So far I've been doing them by hand with 2x2 matrices. It isn't hard, but it takes a while. I have a test coming up in about a week which will have 10 questions that have to be solved in...
  12. N

    Two parallel mirrors are separated by a certain distance

    Your explanation confused me, but I got the answer right answer. I'm not sure why though. I doubled the distance from the object to the first mirror and added that to the distance of the second image from the first mirror.
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    Two parallel mirrors are separated by a certain distance

    Homework Statement Two parallel mirrors are separated by a distance of d = 4 meter. A point object is placed at a position a = 0.4 meter from the mirror 1. How deep is the second image of the object in the mirror 1? How deep is the third image of the object in the mirror 1...
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    Laplace transform of the dirac delta function

    I don't see that formula in my textbook. When I plug in the numbers I get: \frac{2}{s^3} + \frac{e^-s}{s} This is what I did to get my first answer. L[t^2 - t^2 δ(t-1))] \frac{2}{s^3} + \frac{d}{ds} (\frac{d}{ds} (\frac{e^(-s)}{s}) \frac{2}{s^3} +\frac{d}{ds} (\frac{e^-s...
  15. N

    Laplace transform of the dirac delta function

    Homework Statement L[t^{2} - t^{2}δ(t-1)] Homework Equations L[ t^{n}f(t)] = (-1^{n}) \frac{d^{n}}{ds^{n}} L[f(t)] L[δ-t] = e^-ts The Attempt at a Solution My teacher wrote \frac{2}{s^{3}} -e^{s} as the answer. I got \frac{2}{s^{3}} + \frac{e^-s}{s} + 2 \frac{e^-s}{s^2} + \frac{2e^-s}{s^3}
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    Using Laplace Transform to solve a differential equation

    I meant to ask why is my answer different. I don't remember any of the trig identities so I'll have to review them. Thanks for answering my question!
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    Using Laplace Transform to solve a differential equation

    Homework Statement y" + y = 4δ(t-2π); y(0)=1, y'(0)=0 Homework Equations L[f(t-a) U(t-a)] = e^{-as} L[f(t)] L[δ(t-c)] = e^{-cs} The Attempt at a Solution My answer is: cos(t) + 4U(t-2π)sin(t-2π). When I used Wolframalpha it gave me 4sin(t)U(t-2π) + cos(t)
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    Second order ODEs

    Oh, I actually meant could it be solved without changing the equation, but I guess that's a no.
  19. N

    Second order ODEs

    I have another question. Can the undetermined coefficients method be used to solve cauchy-euler equations, or does variation of parameters have to be used?
  20. N

    Second order ODEs

    That's what I assumed, but my teacher believes it's still faster to use variation of parameters. I don't like using that method because I tend to make more mistakes when I integrate e and a trig function. Would this method still be plausible if the right hand side was like this...
  21. N

    Second order ODEs

    I was wondering what a guess would be for the particular solution of the right hand side of an equation if it looked like this: x^{2}y" - 4xy' + 6y = ln(x) My textbook has some specific examples of the right side function along with the corresponding form of the particular solution...
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    Engineering Thevenin Equivalent Circuit: using open/short circuit method

    I wrote the current of the 1 ohm resistor in terms of v and r, I just forgot that it was in parallel with node 2.
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    Engineering Thevenin Equivalent Circuit: using open/short circuit method

    Homework Statement http://i.imgur.com/fSRqw.png Homework Equations V_{th} = V_{oc} The Attempt at a Solution I got the thevenin voltage by using node voltage \frac{V2-40}{5} - \frac{80+2V2}{5} -8 + V2 = 0 (\frac{1}{5} + \frac{2}{5} + 1)V2 = 32 \frac{8}{5}V2 = 32 V2 =...
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    Direction of the torque of the electric force

    Well for my thumb to point outward, the radius should be pointing to the left, but why is it pointing to the left and not towards the right?
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    Direction of the torque of the electric force

    So, one of my fingers points downwards, but I don't know the direction of the radius.
  26. N

    Direction of the torque of the electric force

    Homework Statement http://i.imgur.com/YMuGM.png Homework Equations \tau = F * r The Attempt at a Solution I don't know how to do these types of problems. My professor didn't even go over this. He just said to use that formula to find the answer. I know the electric field...
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    Engineering Finding Thevenin equivalent circuit

    I got 12.025. I used mesh current analysis. I misread the section in my textbook about supermeshes. I thought that supermeshes were only used when an independent current source was shared by two meshes. I didn't know that dependent current sources were acceptable. Boy do I feel stupid; I spent...
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    Engineering Finding Thevenin equivalent circuit

    Yes, I meant short-circuit current. I mixed up the different steps in my textbook. For another method it says when deactivating a current source, it should be replaced with an open circuit. I'll give that a try.
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    Engineering Finding Thevenin equivalent circuit

    That equation you wrote looks similar to the one in my textbook, but it deals with maximum power transfer. The way my professor wanted me to solve for the thevenin resistance was to find the thevenin voltage and divide by the open-circuit current. http://i.imgur.com/OkJNF.png
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