a) Show that from number 1, 2,... , 100 it is possible to select 50 different numbers such that the sum of any two of the selected figures is not 101.

A. In each of Problems 1 through 10, solve the given equations using exact differential equations. 3. v(2uv² – 3)du + (3u²v² – 3u + 4v)dv = 0,when u = 1, v = 1

Solve for x and y

Addalla is preparing for a marathon later in the year. This training session, Addalla takes 20 minutes more than 1.5 times the amount of time it took him to run 25 kilometers the previous time he ran. It took Abdalla 4 hours 56 minutes to complete 25 kilometers this time. Letting t be the amount of time (in minutes) it took Abdalla to run 25 kilometers last time, translate this situation into an equation. Then, determine how long it took Abdalla to run 25 kilometers the last time he trained. (Give your answer in hours and minutes, rounding to the nearest minute.)