)determine if the divergence theorem can be used directly to find the flux of f = r r 2 where r = x i +y j +z k through the following surfaces. s1 is the cylindrical surface of radius 4 and length 10, centered at (6, 0, 0) with its axis parallel to the z-axis, oriented away from its axis. s2 is a sphere of radius 8 centered at the origin, oriented outward. s3 is a sphere of radius 5 centered at (7, 0, 0), oriented outward. s4 is the surface (x − 3)2 + (y − 2)2 + z2 = 16 , oriented outward. s5 is the boundary of the region y2 + z2 ≤ 16, −1 ≤ x ≤ 6 , oriented outward. s6 is the boundary of the region x2 + y2 ≤ 6, 1 ≤ z ≤ 10 , ori

What value of x will make the triangles similar by the sss similarity theorem?

If f(x)=2x-6 and g(x)=3x+9, find (f-g)(x)

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?