for one of my drafting classes I have to design a beam. The beam needs to carry a concentrated load at the midpoint.
some parameters:
4ft span
total materials must weigh under 12oz
Pin reactions at the ends
the person last year that won(highest load) made a simple I joist out of Balsa...
1. Homework Statement [/b]
Given:
C2CL4 + Fe \rightarrow C2H4 + CL- + Fe2+
A reservoir contains 5million gallons of water which is contaminated with 4.2mg/L of Perchloroethene(C2CL4). You want too reduce it to harmless ethene(C2H4) by reacting it with Fe. because of this only about 20g...
that is how I did the problem initially however, the problem says it is in the counterclockwise direction which I would think y goes from 5 to 2, and x from 0 to y-2.
(which is only half of what I did)
Can anyone explain this?
Homework Statement
Calculate \intF dr if C = C1 + C2 where C1 is the line segment from P1(-1,pi,-1) to P2(0,0,0) and C2 is the line segment from P2(0,0,0) to P3(2,0,4)
vectorF= yz i + (xz - e^(z)siny) j + (e^(z)cosy + xy) k
The Attempt at a Solution
Im having problems setting up the...
Homework Statement
Let S be part of the plane 3x + 2y + z =9 lying in the first octant. Calculate the upward flux of vectorF(x,y,z) = x i + xy j + xz k
Homework Equations
z=9-3x-2y
dz/dx=-3
dz/dy=-2
F(dot)(-dz/dx i - dz/dy j + k)
The Attempt at a Solution
x i + xy j + xz k...
Homework Statement
Calculate the total flux of vectorF(x,y,z)=8x^2y i + 6yz^2 j + y^3z k outward through the cube whose verticies are(0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1),(1,1,1), (0,1,1).
Homework Equations
\int\int \widehat{}F \bullet (-partial z/dx i -partial z/dy j +...
Homework Statement
Use Green Theorem to calculate \oint\widehat{}F \bullet d\widehat{}r where C is the closed triangular curve oriented counterclockwise with verticies P1(0,5), P2(0,2) and P3(3,5). vectorF(x,y)= xy^2 i + 4xy j
Homework Equations
The Attempt at a Solution
I first...
Obviously I 'm confused by Parametrizations
the given function is in the form y= f(x,z)
x=cos(theta)
y=lnx
z=sin(theta)
theta from 0 to 2pi
x from 1 to 10
Homework Statement
For what value(s) of the scalar 'a' is the vector field
F(x,y,z)= 2xz i + ay^3 j + (x^2 + y^4) k conservative
The Attempt at a Solution
F1=2xz
F2=ay^3z
F3=(x^2 + y^4)
I used 3D curl test??
1)(partial F2)/(partial dx) - (partial F1)/ (partial dy)= 0-0 =...
Homework Statement
Parametrize a surface obtained by revolving the curve y = lnx, as x goes from 1 to 10 about the y axis
The Attempt at a Solution
y=lnx
x=lnxcos(theta)
z=lnxsin(theta)
vector r(x,theta) = lnx cos(theta) i + lnx j + lnxsin(theta) k
0\leq (theta) \leq 2pi...
Thanks I did not know what to do with factor of 4
so would this be correct?
x=x
y=3cos(theta)
z=6sin(theta)
in vector form
\widehat{}r= x\widehat{}i + 3cos(theta)\widehat{}j + 6sin(theta)\widehat{}k
-3 \leq x \leq 7
do i need to say anything about theta going from 0 to 2pi?
the cross sections of the cylinder perpendicular to the x-axis are circles y^2 + z^2=6^2 correct?
then this would be given parametrically as y=6cos(theta) and z=6sin(theta) right?
Homework Statement
Parametrize the part of the cylinder 4y^2 + z^2 = 36 between the planes x= -3 and x=7
The Attempt at a Solution
radius=6
Parametric equations:
x=x
y=4 + 6cos(theta)
z=6sin(theta)
in vector form
\widehat{}r= x\widehat{}i + (4 + 6cos(theta))\widehat{}j +...
my mistake, should be p^2cos^2(phi) p^2sin(theta)
can this be broken apart:
(Integral rho^4 from 0 to 3)*(Integral Cos^2 phi from 0 to pi/3)*(Integral sin theta from 0 to 2pi)
(1/5rho^5) * (pi/6 + .5sin(pi/3)cos(pi/3)) * (-cos(2pi) - -cos(0))
(48.6)(.2165)(0)=0 ?
I completely stuck
How do I determine what my density function will be?
\int\int\int \delta(x,y,z)\rho^2sin\thetad\rhod\phid\theta
0\leq\rho\leq3
0\leq\leq\pi/3
0\leq\theta\leq2pi
would I use \rho^2??
Homework Statement
W is the solid bounded above by \rho=3 and below by\phi=\pi/3, calculate the mass W if the density at each point is directly proportional to the square of its distance above the xy plane.
The Attempt at a Solution
I am having a difficult time starting out this...
Homework Statement
Point P(x,y,z) lies on the part of the ellipsoid 2x^2 + 10y^2 + 5z^2 = 80 that is in the first octant of space. It is also a vertex of a rectangular parallelpiped each of whose sides are parallel to a coordinate plane. Use Method of LaGrange Multipliers to determine the...
Homework Statement
W is the solid bounded by the three coordinate planes and the surface 4x+2y+3z=16, Calculate Mxz=\int\int\int y dV
Homework Equations
The Attempt at a Solution
the surface 4x +2y +3z=16 is a plane that crosses boundries at (4,0,0), (0,8,0) and (0,0,16/3)...
I have the verticies of the triangle at (2,0), (1,0), and (0,-1)?
wouldn't that mean dy would range from -1 to 2?
the lower part of the triangle dy from -1 to 0, x goes from 0 to y+1
ther upper part, dy ranges from 0 to 2, x goes from 0 to (y-2)/2
do you put an addition sign in between...
b]1. Homework Statement [/b]
Given Domain :\int\intf(x,y)dydx
0\leqx\leq1
x-1\leqy\leq2-2x
reiterate the integrals so the order is reversed
Homework Equations
The Attempt at a Solution
not really sure how to complete,
\int\intf(xy)dxdy
y+1\leqx\leq(2-y)/2
-1\leqy\leq2
Is...
No just need to set up the equations
so the equation would look like:
y'=A
A'=B
B'=(-3y+t^4cos2t) + (A+t^4cos2t) - (6B+t^4cos2t)
not sure why you multiplied B' by 1/2, and also how did you come up with -3B not a positive 3B??
[SOLVED] Transforming 3rd order D.EQ into 1st order
Homework Statement
Transform the following diff eq into a system of first order diff eqs.
2y''' - 6y'' - y' + 3y =t^4cos(2t)
The Attempt at a Solution
heres what I've done so far:
y =A A'=y'
y' =B B'=y''
y'' =C...
[SOLVED] (Methods)Parameters v Undetermined Coefficients
Can anyone tell me why I would use one technique over the other? It seems as though undetermined Coef. is much easier to do but I suppose that comes with limitations?
two equations would then be:
1.(A-6B)sinx=-5sinx
2.(6A+B)cosx=0
1.(A-6B)sinx=sinx
A-6B=-5
-B/6 - 6B=-5
B=-30/37
6Acosx+Bcosx=0
6Acosx=-Bcosx
A=-B/6
A=-(-37/30)/6= 5/37
So general solution:
y=A + Be^6x + Dx + Ex^2 + 5/37sinx -30/37cosx
There seems like there is a different...
you put in a faxtor of x and x^2 ?
y(c)= Ae^0 + Be^6x + Dxe^0 + Ex^2e^0
I used 0 because that would be consitent with the x^3 term-
y(c)=A + Be^6x + Dx + Ex^2
y(p)=Asin(x) + Bcos(x)
y'(p)=Acosx - Bsinx
y"(p)=-Asinx - Bcosx
y'''(p)=-Acosx + Bsinx
y""(p)=Asinx + Bcosx
(Asinx +...
[SOLVED] Variation of Parameters
Homework Statement
y^(4)-6y^(3)=-5sinx
The Attempt at a Solution
I factored this at x^3(x-6)=0
so my r values are 0,6
also using for y(p) Dcosx + Esinx
y=Ae^0 + Be^6x + Dcosx + Esinx ?
y' =6Be^6x -Dsinx + Ecosx
y'' =36Be^6x-Dcosx - Esinx...
wow, why is this problem giving me so much trouble!
so I determined that for the discriminant to equal zero
(a/.5)^2-4(1)(10)=0
a=sqrt10
so b= sqrt10/.5
roots = -(sqrt10/.5)/2
general solution: y=C(1)e^(-sqrt10/.5/2)t + C(2)e^(-sqrt10/.5/2)t
is this correct?
Thanks Tiny Tim!
because mysystem is "critically damped" I need the discriminant to equal 0.
If my initial equation is set up correctly...
x'' + (a/m)x' + 10x = 0
r^2 + (a/m)r + 10
(a/m)^2 - 4(1)(10)=0
a^2/.5^2=40
a^2=10, a=sqrt10 ?
to get the general solution into the form (A+...
huh?
so by saying the system is critically damped the spring will continue to oscillate?
I need to find the roots- if the characteristic equation contains complex or exponential terms we would have repetitive motion?
What is the discriminant of the quadratic equation?
Is my initial 2nd...
[SOLVED] Diff EQ spring question
Homework Statement
a)IF a mass of 0.5kg is attached to a spring with a spring constant of 5(nt/m) and then receives a blow to dislodge it from its equilibrium position, then what is the resistive force coefficient (gamma) if the system is critically damped...
[SOLVED] Diff Eq problem
Homework Statement
y'' - 3y' - 4y= 5e^-x - 3x^2 + 7
Homework Equations
I think I would need to find complimentary solution, then the particular solution using variation of parameters
y=y(c) + y(p)
The Attempt at a Solution
y(c)=
r^2-3r-4=0...