Consider the theorem and its proof below. theorem: if the product of two positive real numbers is greater than 25, then at least one of the numbers is greater than 5. proof: for all positive real numbers a and b, if a s5 and b 5, then ab 25. if a s 5, then ab 5b. since b 55, then ab 25. therefore, if ab > 25, then a > 5 or b> 5. is the proof valid, and which type of proof is used? the proof is valid, and it is a direct proof. the proof is not valid, and it is proof by contrapositive. the proof is valid, and it is proof by contrapositive. the proof is not valid, and it is a direct proof.

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?