Give the Dedekind cuts in ℝ ≥0 corresponding to the following. Your definition should not refer to the elements themselves. i. √10   ii. 3√2   iii. 3√2 + √3

Dd.72.

2. Suppose B is between A and C. Use the segment addition postulate to solve for x. Find the length of each segment. **Draw a picture, it will help you** AB = 6x - 2= BC = 2(x + 3) = %3D AC = 28

9. The average speed (or rate) on a round trip commute between two fixed points having a distance of d is given by the complex rational expression: 2d Here, ri and ra are the speed (or rates) on the outgoing and return trips, respec- tively. Using that answer the following: a) Simplify the complex rational expression and write as a single fraction. (Hint: It will only contain the ri and r2 terms) b) Find your average speed if you drive to campus averaging 30mph and re- turn home on the same route averaging 40mph. Use the simplified rational expression from (a).