Three identical stars of mass M form an equilateral triangle that rotates around the triangle’s center as the stars move in a common circle about that center. The triangle has edge length L. What is the speed of the stars? b.) What is the period of revolution? c.) What is the total potential energy of the 3 star system? Express your answers in terms of the star mass M and triangle edge length L. Hint: Draw a diagram showing the gravitational forces on each star. d.) Find the gravitational force on a single star due to the gravitational attraction of the other two stars, (magnitude and direction). Hints: the 2nd law for a single particle orbiting a planet i.e. Fg = M v 2 /R. You will need to express R in terms of the triangle edge length L. Use v T = 2πR to find the period. it is a symbols-only problem. All work must be done in symbols. There are no numbers.

One of the basic motivations behind the Minimum Spanning Tree Problem is the goal of designing a spanning network for a set of nodes with minimum total cost. Here we explore another type of objective: designing a spanning network for which the most expensive edge is as cheap as possible.

Specifically, let G = (V, E) be a connected graph with n vertices, m edges, and positive edges costs that are all distinct. Let T = (V, E0 ) be a spanning tree of G; we define the bottleneck edge of T to be the edge of T with the greatest cost.

A spanning tree T of G is a minimum-bottleneck spanning tree if there is no spanning tree T 0 of G with a cheaper bottleneck edge.

(a) Is every minimum-bottleneck tree of G a minimum spanning tree of G? Prove or give a counterexample.

(b) Is every minimum spanning tree of G a minimum-bottleneck tree of G? Prove or give a counterexample.

Give examples of how "race" is employed in everyday life that reveals how powerful it is, or that reveals that it is a "social construction."
Be sure to engage with assigned readings and other learning materials below. (500 words or more)(copy paste links in the browser)

In our readings, pay attention to how the “Asian race” has been produced, and how it intersects with Asian religions and what implications that may have for Asians in the United States.

Moreover, think and rethink what you know about race, and engage with the idea of race as a social construction. What does this mean?

Reading 1 link https://www.dropbox.com/s/okuoy59zeuqh4sq/Religion%20Race%20and%20Orientalism--JLEE.pdf?dl=0

Reading 2 link https://www.dropbox.com/s/okuoy59zeuqh4sq/Religion%20Race%20and%20Orientalism--JLEE.pdf?dl=0

video 1 link https://www.youtube.com/watch?v=yHpWzZh2xA4

video 2 link https://www.youtube.com/watch?v=zwHadEXkbyw

Who do you think are the "sellers" of domestic currency? Why do they sell domestic currency? You may choose to list several different possible sellers (list seller categories).

1.List down at least 3 Filipino entrepreneurs and examine their personal entrepreneurial competencies.

2. List down at least 3 competencies and explain how this competencies help them to success.

PART 1: LIST THE FOUR COMPONENTS OF THE “REST TEST” WHICH PERTAINS TO ETHICAL DECISION MAKING AND DISCUSS THEIR MEANING.

PART 2: LIST THE SIX COMPONENTS OF THE KOHLBERG MODEL AND DISCUSS EACH.

Write a Racket function that will take a list of numbers as a parameter and return true if they all are positive, and false otherwise. You are NOT required to check the type of elements in the list.

(please do on racket language)

Write a c++ member function that attempts to insert a NON DUPLICATE element to a doubly linked list, After the attempted insertion return the SIZE of the doubly linked list whether or not the insertion was successful.

Many organizations limit the number of expense (cost) centers.

List three reasons for wanting to limit cost centers.

List three ideas for eliminating or reducing the size of an existing cost center.