project3

14a. Create a graph that models the bordering relationships among the states shown in this map. Use vertices to represent the states and edges to represent common borders. (Ch 14.1 Q14)

Hint: Use an online graphing tool like this one to draw your graph:

https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Graph-Creator/

14b. Draw a graph that models the connecting relationships in the following floor plan. Use vertices to represent the rooms and the outside, and edges to represent the connecting doors. Remember to explain your reasoning.

14c. Consider this graph:

· What is the degree of each vertex in the graph?

· Which vertices are adjacent to vertex F?

· Describe two paths that start at vertex A and end at vertex F.

· Describe a circuit that starts and ends at vertex F.

Remember to explain how you know each answer.

14d. Using the following weighted graph,

· Find the total weight of the six possible Hamilton circuits.

· Use the Brute Force Method to find the optimal solution.

5a. In each of the following examples, state the name of the property illustrated and explain what the property means. (5.5 Q30-34)

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5b. For the following expression, name the property that is used to go from step to step each time (why?) occurs.

5c. Consider an arithmetic sequence with the first term and common difference .

· First, write the first six terms of the sequence.

· Use the formula for the general term, to find .

· What does the term “common difference” mean in your own words?

Explain your thinking.

5d. Determine whether each of the following sequences is arithmetic or geometric. Then find the next two terms. How do you know the difference? Explain your thinking.

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