For each of the following vector fields f, decide whether it is conservative or not by computing curl f. type in a potential function f (that is, ∇f=f). assume the potential function has a value of zero at the origin. if the vector field is not conservative, type n.1. f(x, y)=(-6x+5y)i+(5x+10y)j
2. f(x, y,z)=-3xi-2yj+k
3. f(x, y)=(-siny)i+(10y-3xcosy)j
4. f(x, y,z)=-3x^2i+5y^2j+5z^2k

1,2 and 4 are conservatives

3 is not conservative

Step-by-step explanation:

We calculate  the Curl F

Remember that:

        Curl F = <>

1. Curl F = <0,0,5-5> = <0,0,0>

  The potential function f so that  ∇f=F

  f(x,y,z) =

  Then F is conservative

2. Curl F = < 0, 0 ,0>

  The potential function f so that  ∇f=F

  f(x,y,z) =

  Then F is conservative

3. Curl F = <0 ,0, 10+3xsin(y) - (-cos(y))>

              = <0 ,0 , 10 +3xsin(y) + cos(y)<

 How the field's divergence is not zero the vector field is not conservative

4. Curl F = <0, 0, 0>  

  The potential function f so that  ∇f=F

  f(x,y,z) =    

   Then F is conservative

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

the correct answer is x/3+10≥32

hope this !