Category: Mathematics

This project looks at the thickness of nonplanar graphs.  Thickness is a difficult topic due to the lack of theoretical results.  However, an investigation into the thickness of nonplanar graphs offers excellent insight into planar graphs.  Below are the specific requirements for Project 2.

Use Theorem 4.11 on page 90 to help with the requirements.
– Select and discuss a graph, G, with thickness 2
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form G
– Select and discuss a graph, H, with thickness 3
— Show the graph and provide all of the descriptive information
— Show the planar graphs that can be superimposed to form H
– Select and discuss a maximal planar graph with 8 vertices
— Show the graph and provide all of the descriptive information
— Discuss how the addition of a single edge creates a graph of thickness 2
— Show the planar graphs that can be superimposed to form the graph with its additional edge
– Discuss some generalizations about graphs of thickness 2
— Let us know what you learned during this project
— Provide additional graphs as required

A few notes about format: use MS PowerPoint for your presentation; develop a presentation that is 10-20 slides in length; incorporate audio files into your presentation in order to explain your work; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and select fonts, backgrounds, etc. to make your presentation look professional.

1. During the year, Coronado Boat Yard has incurred manufacturing costs of $420,000 in building three large sailboats. At year-end, each boat is about 70 percent complete. How much of these manufacturing costs should be recognized as expenses in Coronado Boat Yard’s income statement for the current year?
2. A company that assembles trucks produces 60 trucks during the current year and incurs $4.5 million of material, labor, and overhead costs. Fifty-three trucks were sold during the year and each is allocated the same amount of costs. How much of the $4.5 million assembly costs should appear on the company’s income statement for the current year?  (Enter your answers in dollars and not in millions of dollars.)
3. During the current year, the cost of direct materials purchased by a manufacturing firm was $340,000, and the direct materials inventory increased by $65,000. What was the cost of direct materials used during the year?
4. Road Warrior Corporation began operations early in the current year, building luxury motor homes. During the year, the company started and completed 50 motor homes at a cost of $60,000 per unit. Of these, 48 were sold for $105,000 each and two remain in finished goods inventory. In addition, the company had six partially completed units in its factory at year-end. Total costs for the year (summarized alphabetically) were as follows.

Direct materials used

$

728,000

Direct labor

908,000

Income tax expense

100,000

General and administrative expenses

500,000

Manufacturing overhead

1,510,000

Selling expense

Required:

a. Compute the total manufacturing costs charged to work in process for the current year.

b. Compute the cost of finished goods manufactured for the current year.

c. Compute the cost of goods sold for the current year.

d. Compute the gross profit on sales for the current year.

e. Compute the ending inventories of (1) work in process and (2) finished goods for the current year.

a.

Total manufacturing costs

b.

Cost of finished goods manufactured

c.

Cost of goods sold

d.

Gross profit on sales

e-1

Ending inventory of work in process

e-2

Ending inventory of finished goods

This week focuses on applications of geometry. Respond to the following in a minimum of 175 words:

• How would you explain to a classmate the difference between perimeter and area of two-dimensional shapes?
• How about the difference between surface area and volume of three-dimensional shapes?
• What examples or activities would you use to help a classmate understand the differences?

1. A bird species in danger of extinction has a population that is decreasing exponentially (A = A0e^kt). Five years ago, the population was at 1400 and today only 1000 of the birds are alive. Once the population drops below 100, he situation will be irreversible. When will this happen?
2. According to the U. S. Bureau of the Census, in 2000 there were 35.3 million residents of Hispanic origin living in the United States. By 2010, the number had increased to 50.5 million. The exponential growth function A = 35.3e^kt describes the U.S. Hispanic population, A, in millions, t years after 2000.

a. Find k, correct to three decimals places.

b. Use the resulting model to project the Hispanic resident in population in 2015.

c. In which year will the Hispanic resident population reach 70 million?

https://www.ted.com/talks/chris_anderson_technology_s_long_tail%20

describe the graph you selected from the video on technology’s long tail including:

• What does the graph show?
• What values are on the y- and x-axis?
• What is the overall pattern displayed on the graph?
• Be sure to mention all key points on the graph as presented.
• Write the two points you selected as ordered pairs and determine the slope between these two points. Be sure to show the math you used to compute the slope value.
• Identify the y-intercept of the graph you selected. If you selected a reasonable value for the y-intercept, explain why you chose that value, and use it to write an equation for the line in y=mx+b form.
• Interpret the slope as a rate of change and explain what this means in terms of change in both variables.
• Make a prediction for the year 2025, on your graph, using the slope value as a rate of change, and explain whether or not you feel the prediction is reasonable. Explain why.