Find the circulation and flux of the field Bold Upper F equals x Bold i plus y Bold j around and across the closed semicircular path that consists of the semicircular arch Bold Bold r 1 (t )equals (a cosine t )iplus (a sine t )j, 0 less than or equals t less than or equals pi, followed by the line segment Bold r 2 (t )equals t Bold i, negative a less than or equals t less than or equals a. The circulation is nothing. (Type an exact answer, using pi as needed.) The flux is nothing.

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)