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    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.

    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...
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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

    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

    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

    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

    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

    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

    Homework Statement Find the Thevenin resistance. http://i.imgur.com/XoEfy.png Homework Equations Rth =Vex/Iex The Attempt at a Solution I found that the thevenin voltage is 869.304mV. I read in my textbook that in order to find the thevenin resistance in a circuit that contains a...
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    Engineering Finding a specific current in a circuit using Mesh current analysis

    Homework Statement Develop the mesh-current matrix equation for the circuit. http://i.imgur.com/tvZA0.png Homework Equations ƩV_{n} = 0 The Attempt at a Solution I used Mesh current analysis to find 4 equations, but the equations for the first and second mesh are not related...
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    Using node-voltage analytical technique

    Homework Statement Calculate the voltage at each of the extraordinary nodes (V1 – V3), and the current through each of the six resistors. http://i.imgur.com/VbZQH.png Homework Equations KCL: ƩIn = 0 V=ir I=A^{-1}B \Delta = a11C11 + a12C12 + a13C13 A^{-1} = \frac{adjA}{\Delta}...
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    Determining power across a certain device.

    Homework Statement The voltage across and current through a device are given by: v(t)= 5cos(4∏t)V i(t) = 0.1cos(4∏t)A determine the instantaneous power p(t) at t=0 and t = 0.25s Homework Equations p=vi The Attempt at a Solution for t=0 I got p=0.5W for t=0.25 I got p =...
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    Modify input file name and print as output [C]

    I have a question, how can I make an output file that takes the name of the input file and replaces the .txt extension with "_out.txt"? For example, an input file with the name “new.txt” would result in an output file named new_out.txt”. my friend told me to use strcat, but that just adds...
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    First order separable differential equation

    Homework Statement x\frac{dy}{dx} = 4y Homework Equations I'm not sure if there is a specific equation for these type of problems. My professor just says to separate the two different variables and then integrate them with respect to x. The Attempt at a Solution \frac{1}{4y}...
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    Voltage and current division

    Homework Statement http://i.imgur.com/XbMaK.png Use voltage and current division to determine V_{0} in the circuit given that V_{out} = 0.2V. Homework Equations v_{i} = \frac{R_{i}}{R_{eq}} * v_{s} i_{n} = \frac{R_{eq}}{R_{n}} * i_{s} The Attempt at a Solution I got \frac{236}{23} for the...
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    Engineering Simplifying a circuit in order to find the current

    Homework Statement I solved my original question so I posted another one. http://i.imgur.com/dpevY.png Find R_{eq} at terminals (c,d) Homework Equations R_{eq} in series = Ʃ R R_{eq} in parallel = \frac{1}{R_{1}} + \frac{1}{R_{2}} + ...+ \frac{1}{R_{n}} The Attempt at a Solution I don't...
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    Using Integration by parts

    Homework Statement ∫\frac{1}{x^{2}*ln(x)} Homework Equations ∫udv = uv-∫vdu u=ln(x) du = \frac{1}{x}dx dv = x^{2}dx v = \frac{x^{3}}{3} The Attempt at a Solution Using the above formula I got \frac{x^{3}}{3}*ln(x) - \frac{x^{3}}{9} + C Am I doing this correctly or do I...
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    The amount of power supplied/received by the dependent current source

    Homework Statement http://imgur.com/jsIWS Homework Equations Ʃ V_{n} = 0 Ʃ I_{n} = 0 v = ir The Attempt at a Solution I combined the two 2Ω resistors into a single 4 Ω resistor because they're in series. Then I tried to use KCL but I got 2 unknowns in one equation. 0.2A + \frac{Vi}{4} = I
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    Engineering Using Kirchhoff's laws to find current in a circuit

    Homework Statement Use KCL and KVL to determine the currents I1 to I3 in the circuit below: Homework Equations Ʃv_{n} = 0 Ʃi_{n} = 0 v=ir The Attempt at a Solution I got two different answers for I_{1} using the two different laws. I'm not sure if I'm doing it right. KVL @ loop 1: -18 + 6...
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    What is the energy dissipation through the wire?

    Homework Statement A 3 m long copper wire that has a diameter of 6 mm is connected to a 9 V battery. a) What is the current through the wire? b) If wire a was connected to a battery for 1 second, how much energy would the wire dissipate? Homework Equations A = \pir^{2} R = \rho\frac{L}{A} i =...
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    Taylor series

    Homework Statement Find the first 3 non-zero terms of the Taylor polynomial generated by f (x) = x^{3} sin(x) at a = 0. Homework Equations f^{n}(x) * (x-a)^{n} / (n!) The Attempt at a Solution I got the question wrong: my answer was 1/3! + 1/5! + 1/7! Here is the answer below. I...
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    Exam question

    Homework Statement This was a question on my test. I had to choose the direction of the acceleration vector for each position. I was wondering if I chose the correct answers. Homework Equations a = gsinθ ƩF_{y} = N_{1S}( normal force) - W_{1E} ( weight force) The Attempt at a...
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    Two balls on a rotating disk.

    Homework Statement Homework Equations I=mr^{2} L=ωI ω=\frac{L}{I} The Attempt at a Solution I thought that since the moment of inertia was larger for the ball on the outside its angular speed would be slower. So then it would take longer to hit the wall.
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    Find the angular velocity

    Homework Statement A ring (mass 2 M, radius 1 R) rotates in a CCW direction with an initial angular speed 1 ω. A disk (mass 2 M, radius 2 R) rotates in a CW direction with initial angular speed 4 ω. The ring and disk "collide" and eventually rotate together. Assume that positive angular...
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    Rotational motion of a spinning disk

    Homework Statement A spinning disk is rotating at a rate of 30 rad/s in the counterclockwise direction. The disk is slowing down at a rate of 6 rad/s2. Find the angle through which the disk has turned after 3 s in radians, degrees, and revolutions. Homework Equations θ=θi + ωi*t + αt^2...
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    Integral of tan^3(x)

    Homework Statement ∫tan^{3}x dx Homework Equations tan^{2}x+1 = sec^{2}x tan^{3}x = tan^{2}x * tan(x) The Attempt at a Solution ∫tan^{2}x * tan(x) dx ∫(sec^{2}x -1 ) tan(x) dx ∫(sec^{2}xtan(x) -∫tan(x) ∫u du - sec^{2}x u^{2}/2 - sec^{2}x tan^{2}x/2 - sec^{2}x
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    The integral of cot^3(x)

    Homework Statement Integrate ∫cot^{3}(x) Homework Equations u*v-∫vdu The Attempt at a Solution I used the integration by parts formula and I got: cot^{3}(x)(ln|sin(x)|)-∫ln|sin(x)|-x-cot(x)dx I don't know how to integrate the integrand.
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    Finding the total area of the shaded region.

    Homework Statement http://img545.imageshack.us/img545/6260/hardproblem.png [Broken] Homework Equations 1. First I solved for y 2. I put it in the form f(x)-(g(x) 3. Then I integrated The Attempt at a Solution The answer in my book says it is ∏/2. I don't think I'm...
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    Evaulating this Integral

    Homework Statement http://img528.imageshack.us/img528/356/hwhelp.png [Broken] Homework Equations http://img407.imageshack.us/img407/3696/uanddu.png [Broken] The Attempt at a Solution This is the answer I got. I was wondering how du replaces the circled part of the question...
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