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1. ### Beam Design Question?

sorry, simply supported rigid beam, reaction only in the y direction, no x or moment
2. ### Beam Design Question?

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...
3. ### How many grams of Fe needed?

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...
4. ### Greens theorem-help setting up correct integral

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?
5. ### Line Integrals

Great idea, thanks for your help
6. ### Line Integrals

its late...what else can i say I don't know what to use for t going from 0 to 1 y=pi t + pi y(0)=pi y(1)=2pi y=pit - pi y(0)=-pi y(1)=pi t - pi=0
7. ### Line Integrals

x=t-1 y=pit^2 z=t-1
8. ### Line Integrals

x=t-1 y= pi t + t z=t-1 t goes from -2 to -1, would that work?
9. ### Line Integrals

that it is path independent or conservative?
10. ### Line Integrals

dF2/dx - dF1/dy =0 z-z=0 dF3/dy - dF2/dz =0 (-e^zsiny + x) + (-x + e^zsiny) = 0 dF1/dz - dF3/dx = 0 y-y=0 Curl test?? how does that help?
11. ### Line Integrals

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...
12. ### Calculate the upward flux

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...
13. ### Total Flux through a cube

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 +...
14. ### Greens theorem-help setting up correct integral

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...
15. ### Parametrize a surface

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
16. ### Vector field, Conservative?

yes it should be ay^3z j, Thanks!
17. ### Vector field, Conservative?

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 =...
18. ### Parametrize a surface

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...
19. ### Parametrize a cylinder

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?
20. ### Parametrize a cylinder

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?
21. ### Parametrize a cylinder

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 +...
22. ### Tough Integral problem

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 ?

24. ### Tough Integral problem

z=\rhocos\phi z^2=(\rhocos\phi)^2 ??
25. ### Tough Integral problem

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??
26. ### Tough Integral problem

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...
27. ### Lagrange Multipliers, calc max volume of box

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...
28. ### Help setting up triple integral

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)...
29. ### Reversing integration

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...
30. ### Reversing integration

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...
31. ### Leplace transform

but its t^1, so n=0, t^0+1=t^1 right?
32. ### Leplace transform

Homework Statement y"+4y=7t , y(0)=-1, y'(0)=3 The Attempt at a Solution L{y} + 4L{y} = 7L{t} (s^2L{y} - sy(0) - y'(0)) + 4L{y} = 7L{t} s^2L{y} - s(-1) - 3 + 4L{y} = 7(0!/s^(0+1)) L{y}(s^2 + 4) = 7(0!/s^(0+1)) - s + 3 = ((-s+3)s + 7)/s...
33. ### Transforming 3rd order D.EQ into 1st order

I see I forgot the coefficent 2 before y''', still can't see how you get -3B and not positive 3B
34. ### Transforming 3rd order D.EQ into 1st order

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??
35. ### Transforming 3rd order D.EQ into 1st order

[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...
36. ### Variation of Parameters

-5/37sinx +30/37cosx
37. ### (Methods)Parameters v Undetermined Coefficients

Thanks for the explanation
38. ### (Methods)Parameters v Undetermined Coefficients

[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?
39. ### Variation of Parameters

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...
40. ### Variation of Parameters

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 +...
41. ### Variation of Parameters

[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...
42. ### Diff EQ spring question

Thanks for all your help-much appreciated
43. ### Diff EQ spring question

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?
44. ### Diff EQ spring question

OK, then my quadratic equation must be set up incorrectly? any insight on that would be helpful
45. ### Diff EQ spring question

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+...
46. ### Diff EQ spring question

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...
47. ### Diff EQ spring question

[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...
48. ### Solved: Diff Eq Problem y'' - 3y' - 4y= 5e^-x - 3x^2 + 7

[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...
49. ### Tough Diff EQ problem

the sqrt of -1= 1i correct-----ohhhhh wow that changes things: e^(0)cos(x)+e^0sinx= C(3)cosx + C(4)sinx(x) y=c(1)e^3x + c(2)e^-3x + c(3)cosx + c(4)sinx -7/60xe^-3x ??
50. ### Tough Diff EQ problem

dumb mistakes! r=+/- 3, and 1+i Y(c)=Ce^3x + Ce^-3x + Ce^(x)cosx + Ce^(x)sin(x) Y(p) =Axe^-3x y'(p) =Ae^-3x - 3Axe^-3x y''(p) =-3Ae^-3x - 3Ae^-3x + 9Axe^-3x y'''(p) =9Ae^-3x + 9Ae^-3x + 9Ae^-3x - 27Axe^-3x y''''(p)=-27Ae^-3x -27Ae^-3x - 27Ae^-3x - 27Ae^-3x + 81Axe^-3x= 81AXe^-3x -...