## mattt9 3 years ago 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))

1. helloimjared

Are you building a time machine?

2. mattt9

hahahha i wish.

3. mattt9

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

4. helloimjared

hahaha

5. elica85

what is the question? find the value?

6. mattt9

yes exactly

7. mattt9

it will be decimal

8. elica85

have you set up the triple integral?

9. mattt9

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

10. mattt9

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

11. mattt9

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

12. mattt9

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

13. elica85

is f=|F|?

14. elica85

or was it suppose to be F

15. mattt9

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

16. mattt9

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

17. mattt9

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

18. elica85

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

19. elica85

so you got f?

20. mattt9

no, I wish.. aha

21. mattt9

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

22. mattt9

because they are all long trigonmetric quantities very prone to mistakes

23. elica85

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

24. mattt9

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

25. mattt9

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

26. mattt9

27. elica85

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

28. mattt9

Okay thank you :)

29. jeff1949

How can i contact mattt9 to discuss a maths problem?