Two students start a club the first week of school. each member invites three new members the second week of school. each of these new members then invites three additional members the following week. if the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks? (note: this is an example of a mathematical series)

242

Step-by-step explanation:

Given that two students start a club the first week of school. Each member invites three new members the second week of school.

Since each new member invites 3 additional members the following week, we have

I week = 2 students

II week= 2x3 +2 = 8 students( 2 old and 6 new)

III week = 8+6x3 = 26 students (8 old + 18 new)

Iv week = 26+18x3 = 80

V week = 80+54x3 = 242

Note:   Note that new members invite 3 addl members already one week old members will not bring new additions.

1) Kinetic energy of the truck 1 is 600,000 joules.

Kinetic energy of the truck 2 is 1,837,500 joules.

2 a)Potential energy of truck 1 is 646,800 Joules.

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.

Step-by-step explanation:

Mass of the truck 1 and truck 2,m = 3000 kg

Velocity of the truck 1, = = 20 m./s

Velocity of the truck 2, = 35 m./s

1. Kinetic energy of the truck 1:

Kinetic energy of the truck 2:

2.a) Energy loose by the truck 1:

Initial height of the truck on the hill = 22 m

At that height potential energy will be maximum:

Potential energy of truck 1 at that height =

b) Energy lose by the truck 1 just got converted into heat and sound energy during the collision.