This exercise determines when two elements of sn are conjugate.

(a) show that for any k cycle (a1, ..ak) e sn, and for any permutation π n, we have hint: as always, first look at some examples for small n and k. both sides are permutations (i. e., bijective maps defined on 11, , show that they are the same maps by showing that they do the same thing.

(b) show that for any two k cycles, (ai. ak) and (bi, b2. . , bk) in sn there is a permutation π e s, such that

Gas mileage actually varies slightly with the driving speed of a car (as well as with highway vs. city driving). suppose your car averages 33 miles per gallon on the highway if your average speed is 54 miles per hour, and it averages 22 miles per gallon on the highway if your average speed is 75 miles per hour. answer parts (a) and (b) below. a. what is the driving time for a 2000-mile trip if you drive at an average speed of 54 miles per hour? what is the driving time at 75 miles per hour? the driving time at 54 miles per hour is nothing hours. (type an integer or decimal rounded to two decimal places as needed.) the driving time is at 75 miles per hour is nothing hours. (round to two decimal places as needed.) b. assume a gasoline price of $3.33 per gallon. what is the gasoline cost for a 2000-mile trip if you drive at an average speed of 54 miles per hour? what is the gasoline cost at 75 miles per hour? the gasoline cost at 54 miles per hour is $ nothing. (round to two decimal places as needed.) the gasoline cost at 75 miles per hour is $ nothing. (round to two decimal places as needed.)