Question

let f be the outward flux of the vector field F = (c_1x,c_2y,c_3z) over the torus: x=cosu(1.86+0.9cosv); y=sinu(1.86+0.9cosv); z=0.9sinv;
for 0<=u<=2pi; 0<=v<=2pi, where c_1, c_2, c_3 are positive constraints. then the value of cot(f/(c_1+c_2+c_3))

Answer 1

Are you building a time machine?

Answer 2

hahahha i wish.

Answer 3

I would travel 3 months forward in time so i can be done calculus IV

Answer 4

hahaha

Answer 5

what is the question? find the value?

Answer 6

yes exactly

Answer 7

it will be decimal

Answer 8

have you set up the triple integral?

Answer 9

no its a ridiculous amount of work. and it should only be double? im not changing the coordinates. when you reparametrize it you get r(u,v) =x(u,v)i +y(u,v)j +z(u,v)k where x(u,v), etc. are those functions for x y and z above

Answer 10

then the integral should be F(dot)r_u X r_v/|r_u X r_v|

Answer 11

where thats the vector cross product operator
and r_u and r_v are the partial derivatives of r with respect to u and v

Answer 12

and the bounds can be the same i.e. 0-->2pi for both u and v

Answer 13

is f=|F|?

Answer 14

or was it suppose to be F

Answer 15

no f is the flux .. f is the result of the integral you solve

Answer 16

F is the vector field that you put inside the integral to solve the flux

Answer 17

essentially since they don't give you values for the constants, they should somehow cancel out in the end

Answer 18

sorry, i'm making it more work for you. but no one's answering anyways right?

Answer 19

so you got f?

Answer 20

no, I wish.. aha

Answer 21

its those cross products
that literally take up 2 pages of work

Answer 22

because they are all long trigonmetric quantities very prone to mistakes

Answer 23

o yikes i can't commit to that now. i wish, it would be good practice

Answer 24

i figured out r_u X r_v.. but its taking the absolute value that im just too scared to try. because you have to square each i j k term and put them under a root sign

Answer 25

yeah I understand aha, this was really a shot in the dark trying to get help on here. I can't imagine anyone wanting to attempt this question. It's the last one I have left on my assignment. Our calculus professor is straight up unfair, literally 10-30 hours of calc a week

Answer 26

thanks for reading by the way though, your efforts are appreciated

Answer 27

i was more interested in someone else answering, i only went to calc III. good luck, there are a lot of helpful people on here. i would post again so they see it

Answer 28

Okay thank you :)

Answer 29

How can i contact mattt9 to discuss a maths problem?