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 ≤...
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...
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...
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...
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}
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)
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...
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 =...
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...
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...
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...
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}...
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 =...
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...
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}...
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...
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...
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...
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
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...
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 =...
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...
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...
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.
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...
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...
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.
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...
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...