# Essay on Discrete Math Week 2 Assignment

Part I:

Suppose you are developing a statistical database in which information about professional football teams and records are stored.

Consider the following 2 sets of data that list football teams and quarterbacks:

D = {Jets, Giants, Cowboys, 49ers, Patriots, Rams, Chiefs}

Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning} 1. Using D as the domain and Q as the range, show the relation between the 2 sets, with the correspondences based on which players are (or were) a member of which team(s). (You can use http://www.pro-football-reference.com to find out this information). Show the relation in the following forms:

Set of ordered pairs

{(Jets, Joe Namath), (Giants,

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Mathematical sequences can be used to model real life applications. Suppose you want to construct a movie theater in your town. The number of seats in each row can be modeled by the formula C_n = 16 + 4n, when n refers to the nth row, and you need 50 rows of seats. (a) Write the sequence for the number of seats for the first 5 rows

C(1) = 16 + 4 (1) = 16 + 4 = 20 seats in the first row

C(2) = 16 + 4 (2) = 16 + 8 = 24 seats in the first row

C(3) = 16 + 4 (3) = 16 + 12 = 28 seats in the first row

C(4) = 16 + 4 (4) = 16 + 16 = 32 seats in the first row

C(5) = 16 + 4 (5) = 16 + 20 = 36 seats in the first row

The sequence for the number of seats in the first 5 rows would be the following;

20, 24, 28, 32, 36

(b) How many seats will be in the last row?

There are 50 rows, so n = 50

C(50) = 16 + 4 (50) = 16 + 200 = 216 seats in the last row

The last row will have 216 seats.

(c) What will be the total number of seats in the theater?

From our MATH 203 Live Chat Session #4 on Wednesday evening 26 November 2014 we learned that the Sum of terms in a Sequence has the following formula;

Sn = [ n (a1 + an ) ] / 2

So with that said n = 50 for the number of rows in the theater.

S50 = [ 50 (a1 + an ) ] / 2

So in this case a1 is the first row which equals 20 seats in that