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    Evaluate infinite sum using Parseval's theorem (Fourier series)

    Homework Statement Show that: \sum_{n=1}^{\infty}\frac{1}{n^4} = \frac{π^4}{90} Hint: Use Parseval's theorem Homework Equations Parseval's theorem: \frac{1}{\pi}\int_{-\pi}^{\pi} |f(x)|^2dx = \frac{a_0^2}{2}+\sum_{n=1}^{\infty}(a_n^2+b_n^2) The Attempt at a Solution I've been trying to solve...
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    Find centroid of region - triple integrals, need help please!

    Thanks for the method confirmation, I tried it again, very carefully, and it worked! :)
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    Find centroid of region - triple integrals, need help please!

    Homework Statement Find the centroid x,y,z of the region R cut out of the region 0<=z<=5sqrt(x2+y2) by the cylinder x2+y2=2x. Homework Equations x2+y2 = r2 x= rcosθ y= rsinθ The Attempt at a Solution Centroid x being Mx/m I'm guessing I've been working on this problem...
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    Motion in curves - Find radial and circumferential components of V and A

    Yeah, but say I do Vr = V * Ur I would get Vr = (2t i + 2 j) * (cosθ i + sinθ j) Vr = 2tcosθ i + 2sinθ j Is that right? It strikes me as odd that the Vr I found has both θ and t in it.
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    Finding partial derivative of a trig function

    cos(x) is equal to cos(-x) Those answers are equivalent. Btw, if you're confused as to what Wolfram Alpha is doing, press the "Show steps" button. Helps out sometimes.
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    Motion in curves - Find radial and circumferential components of V and A

    Homework Statement At time t, a comet has the position R = (t2-1)i + 2tj At t = 2, find the radial and circumferential components of velocity and acceleration Homework Equations Vr = V * Ur Vθ = V * Uθ ar = a * Ur aθ = a * Uθ Ur = cosθ i + sinθ j Uθ = -sinθ i + cosθ j...
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    I don't get this question help me please?

    You have the initial horizontal velocity, and the distance traveled horizontally. Using your equations, you should be able to find the time it takes for the ball to hit the ground. You have all the information you need now. For the vertical "part" of this problem, you know what distance must...
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    Electric field/Equipotentials

    A part of the problem is missing. A diagram most likely.
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    Circulating Charged Particle

    k=0.5mv2 you should know that formula
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    Calculating work done by E field/voltage

    I'm kind of sleepy so i couldnt pinpoint the problem earlier but I'm pretty sure you just used the wrong value of r, thats why I recommended to draw a diagram. its the middle of a square with 10 cm sides so if you do pythagoras you have to use .05m and not .1m like you did
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    Calculating work done by E field/voltage

    yeah, I had just done it and I got -2.55J as the answer right before I posted my reply. here: W=(kQq)/r get it into W=(k)*(Q)/(r)*(sum of qs) form W=(9*10^9)*(-5microC)/(0.0707m) *(.6microC + 2.2microC - 3.6microC + 4.8microC) W=-636396*(4microC) W=-2.55J
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    Calculating work done by E field/voltage

    your method is fine, you must have done a calculation error somewhere. just redo it on a piece of paper.
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    Calculating work done by E field/voltage

    I'm not too sure what you did in your calculations but.. First step is to do a diagram with the 4 charges each at a corner of the square. Then you have to find the potential energy at the center of the square (which is acquired by adding the V=kq/r for each charge). Now that you have the...
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    Free fall help!

    yes the vf will be negative, like i said in my previous reply >_>
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    DC Circuit problem

    Thanks, that definitely helped, but why can't the "simplified path" and the bottom path with the 20 and 5 ohm resistors be treated as if they were in parallel and then simplified further into one path?
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    Free fall help!

    d is actually -239m since it's falling. which means starting from 239 m and falling down to 0m so the change is -239m. the vf you will then calculate is actually negative like the acceleration since, again, it is falling downwards on the y axis
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    DC Circuit problem

    Homework Statement Find a) the potential difference between points a and b b) the current of the 20 ohm resistor I drew the diagram in MS Paint. Should be good enough. http://img188.imageshack.us/img188/6515/circuitf.jpg [Broken] 2. The attempt at a solution I just don't know where to...
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