1- the sum of three numbers is 4, sum of their squares is 10 , and the sum of thier cubes is 22 what is the sum of their fourth powers.
2- 3 men went to a hotel to rent a room, the cost of the room was $30. Each man paid $10 to the bellboy and proceeded to there room. After a little while the bellboy realized that there was a special on rooms that night and the price for the men's room should have been $25. On his way to the men's room to give them back $5 he was puzzled how he was going to split $5 as he had no change. He decided he would give them each $1 and keep the remaining $2 for himself. So each man originally paid $10, but after the bellboy gave each man $1 back, each man paid $9. 9 x 3 = $27 plus the $2 the bellboy put in his pocket equals $29. The original price for the room was $30. Where did the last dollar go?
3- Tow boats facing each other from opposite sides of a river both leave at the same time heading toward each other. Although one boat is traveling at a faster rate than the other, both of their rates are consistent. The first time the boats meet, they are 700 yards from one shore. They pass each other and continue on to the other side of the river, then turn around (with no time loss) and head back toward each other, continuing at their same rates. The second time they meet, they are now 300 yards from the other shore. Assuming there is no current, what is the width of the river.
Please explain your answer
4- Find all positive integers n such that 2ⁿ-1 is a multiple of 3 and (2ⁿ-1)/3 is a divisor of 4m²+1 for some integer m.