Cosmic ray bombardment of the atmosphere produces neutrons, which in turn react with nitrogen to produce radioactive carbon- Radioactive carbon- enters all living tissue through carbon dioxide (via plants). As long as a plant or animal is alive, carbon- is maintained in the organism at a constant level. Once the organism dies, however, carbon- decays exponentially into carbon- By comparing the amount of carbon- to the amount of carbon- one can determine approximately how long ago the organism died. (Willard Libby won a Nobel Prize for developing this technique for use in dating archaeological specimens). The half-life of carbon- is about years. In answering the following questions, assume that the initial quantity of carbon- is milligrams.

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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