Circle constructions – part 1 students guide

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Geometric Constructions

In this lesson, you learned how a compass and straightedge are used to create constructions related to circles. In this assignment, you will use those tools to complete those constructions on your own.

As you complete the assignment, keep this question in mind:

How do you perform constructions related to circles?

Directions

Complete each of the following constructions, reading the directions carefully as you go. Be sure to show all work and insert an image of each construction. If you are unable to take and insert screenshots of the constructions, print this activity sheet and create them by hand using a compass and straightedge.

Your teacher will give you further directions about how to submit your work. You may be asked to upload the document, e-mail it to your teacher, or print it and hand in a hard copy.

Now, let’s get started!

Step 1: Construct a circle through three points not on a line.

a) Construct a circle through three points not on a line using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a circle through three points not on a line by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

Step 2: Construct regular polygons inscribed in a circle.

a) Construct an equilateral triangle inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct an equilateral triangle inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

b) Construct a regular hexagon inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a regular hexagon inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

c) Construct a square inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a square inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

Step 3: Construct tangent lines to a circle.

a) Constructa tangent to a circle through a point on the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, a tangent to a circle through a point on the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

b) Construct a tangent to a circle through a point outside the circleusing the construction tool. Insert a screenshot of the construction here. Alternatively, construct a tangent to a circle through a point outside the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

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July 1, 2023

41) The above figure shows the production possibility frontier for an economy. The point or points that are attainable and production efficient are

A) points B and C.

B) points A, B, and C.

C) point E.

D) points A, B, C, and D.

E) points A and D.

42) The above figure shows the production possibility frontier for an economy. The point or points that are attainable are

A) points B and C.

B) points A, B, and C.

C) point E.

D) points A, B, C, and D.

E) points A and D.

43) The above figure shows the production possibility frontier for an economy. The point or points that are NOT attainable are

A) points B and C.

B) points A, B, and C.

C) point E.

D) points A, B, C, and D.

E) points A and D.

44) In order for Ireland to grow more potatoes, wool production must decrease. This situation is an example of

A) producing at a point that lies beyond the PPF.

B) zero opportunity cost.

C) opportunity benefit.

D) a free lunch.

E) a tradeoff.

45) As we move along the production possibilities frontier,

A) the production of one good increases as the production of the other good decreases.

B) the possibilities of tradeoffs diminish.

C) a tradeoff is not possible because nations need all goods.

D) more of both goods can be produced.

E) less of both goods can be produced.

46) Which of the following statements is correct?

A) If capital is idle, the economy is producing at its full potential.

B) The production possibilities frontier shows that there are no limits to production.

C) A tradeoff is a limit that forces an exchange or a substitution of one thing for something else.

D) Any point on or within the PPF is production efficient.

E) None of the above answers is correct.

47) When a nation is producing on its production possibilities frontier, if more resources are used to produce one good, then the production of other goods

A) must increase.

B) must decrease.

C) must remain the same.

D) must change, but they might increase or decrease.

E) might increase if the nation can produce more efficiently.

48) The negative slope of the production possibilities frontier represents the idea

A) that free lunches are possible.

B) of tradeoffs, that in order to produce more of one good, the nation must produce less of another.

C) of unemployment.

D) of inefficient production.

E) that prices rise as less is produced.

49) A movement from one point on a production possibilities frontier to another represents

A) a tradeoff.

B) a free lunch.

C) full employment of labor but not capital.

D) unemployment.

E) an advance in technology.

50) The saying "There's no such thing as a free lunch," applies

A) when there is some unemployment.

B) on the production possibilities frontier.

C) to unattainable combinations of goods and services.

D) when more of one good can be produced without decreasing production of another.

E) at all points inside the PPF.

July 1, 2023

31) Steve, an HR supervisor at APEX construction, has recently noticed a shortage of skilled workers due to a building boom in the area. He must find new workers quickly because it is uncertain how long the boom will last. He decides to hire nontraditional laborers. The most likely disadvantage of using nontraditional laborers is the:

A) high costs of making reasonable accommodations.

B) additional training that will be necessary.

C) extensive involvement of the EEOC.

D) high advertising costs.

32) Which of the following is primarily associated with hiring external candidates?

A) Lowers training costs

B) Provides new ideas and perspectives

C) Decreases recruitment time and expense

D) Motivates other workers to strive for advancement

33) One of the advantages of promoting internal candidates is:

A) rejuvenating work units.

B) reducing training costs.

C) fostering innovative ideas.

D) reducing employee turnover.

34) Tatiana needs to hire a line manager and has a very small recruiting budget. The firm's current employees don't feel they have many advancement opportunities. It would be best for Tatiana to recruit:

A) internally.

B) externally.

C) former military members.

D) nontraditional workers.

35) Which of the following is most likely a true statement about recruiting?

A) Internal recruiting enhances organizational communication.

B) External recruiting fills positions quickly and inexpensively.

C) External recruiting promotes innovation and new perspectives.

D) Internal recruiting requires developing new organizational policies.

36) Which of the following is most likely a true statement about recruiting employees in a protected class?

A) The recruiting message should be targeted to specific minority groups.

B) All private sector firms are legally required to have an affirmative action policy.

C) Using media that focuses on minorities is an effective way to recruit protected group members.

D) Intense minority competition for jobs ensures a large pool of qualified and motivated applicants.

37) Which of the following must have written affirmative action plans?

A) Non-profit groups

B) Government contractors

C) Privately-held corporations

D) Publicly-held corporations

38) In human resource planning the answer to the question, "How many candidates should we recruit?":

A) is based on the firm's affirmative action plan.

B) comes from the yield ratio calculated in the forecast.

C) is directed by EEO consideration and the size of the labor pool.

D) depends on the state of the labor pool and the current economy.

39) The offer-to-acceptance ratio at Central Manufacturing is 6:1. How many offers will the firm need to make in order to fill 80 positions?

A) 120

B) 240

C) 480

D) 540

40) After an extensive recruiting effort, your company has contacted 225 interested individuals. At the application deadline, you have received 75 applications. What is your contact-to-applicant ratio?