Phase 2 Task 2 Project TEMPLATE

Phase 2 Task 2 Project TEMPLATE

Name______

VIEW LIVE CHATS 3 and 4 FIRST!!

Task Type: Individual Project Deliverable Length: See Assignment Details
Points Possible: 100

Task Background: 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, 49’ers, Patriots, Rams, Chiefs}
Q = {Tom Brady, Joe Namath, Troy Aikman, Joe Montana, Eli Manning}

NOTE: (You can also use to find this information, but here it is as well :)

The following list gives you the relationships (mapping) between team and QB.

Jets – Joe Namath

Giants – Eli Manning

Cowboys – Troy Aikman

49’ers – Joe Montana

Patriots – Tom Brady

Rams – Joe Namath

Chiefs – Joe Montana

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 on which team. Show the relation in the following forms:
Set of ordered pairs (20 points)

{(Jets ,Joe Namath),(Giants,Eli Manning),(Cowboys,Troy Aikman),(49’ers,Joe Montana),(Patriots,Tom Brady),(Rams,Joe Namath),(Chiefs,Joe Montana)}

Directional graph (like the pictures draw in class in our live chats – see HINT below). (20 points)

Is the relation a function? Explain. (10 points)

This is a function as for each element in domain there is one and only one element in range.

Now, use set Q as the domain, and set D as the range (reverse). Show the relation in the following forms:
Set of ordered pairs (20 points)

{(Joe Namath,Jets),(Eli Manning,Giants),(Troy Aikman,Cowboys),(Joe Montana, 49’ers),(Tom Brady,Patriots),(Joe Namath,Rams),(Joe Montana,Chiefs)}

Directional graph (20 points)

Is the relation a function? Explain. (10 points)

Joe Namath and Joe Montana from domain map on two-two elements in the range which contradicts with the definition of function. Thus this relation is not a function.

Part 2: 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

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

Hint: C(25) = 16 + 4(25) = 16 + 100 = 116 seats in the 25th row

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

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

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

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

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

Sequence for the number of seats for the first 5 rows will be

20, 24, 28, 32, 36

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

There are 50 rows. Put n = 50

C(50) = 16 + 4(50) = 16 + 200 = 216 seats

There will be 216 rows in the last row.

Hint: these concepts are in sequences and series

Sum of n terms of arithmetic sequence

Where a1 is the first term and an is the nth term

We want to find sum of number of seats in 50 rows

Total number of seats in the theater is 5900.