]give a proof by contradiction: let g be any directed graph in which every pair of nodes u and v has exactly one edge (either uv or u v but not both), and let w be a node with highest out-degree. then every node is reachable from w by a path of length 3 2.

Step 1: choose your topics review the project milestone reflections you submitted for modules 1 through 4. choose the one major idea or concept from each module that you feel most applies to your life. in addition, choose an important concept from module 5 that applies to your life. step 2: write your guidebook for each module: write a catchy headline that clearly and concisely sums up your chosen idea or concept write a brief explanation that includes a description of the concept, why it is important, and how it can be applied to your life to make a positive impact choose an exciting, powerful, or engaging image that illustrates your concept remember, you are writing one for each module, so you will have a total of five headlines, five descriptions, and five images. step 3: design your guidebook choose a format to present your digital guidebook. there are many 21st century tools available for creating and submitting your work in the online environment. for more information on tools your school uses, contact your instructor or visit the web 2.0 tools area.

Let r be a robotic arm with a fixed base and seven links. the last joint of r is a prismatic joint, the other ones are revolute joints. give a set of parameters that determines a placement of r. what is the dimension of the configuration space resulting from your choice of parameters?

Sports and entertainment class, your goal is to increase attendance and make a profit for a game by getting your team on a winning track with total salaries less than $3,000,000