1. Solve the recurrence relations (a) a, = an-1, a1 = 1; (b) an = 5an-1 - 6an-2, a1 = -1, az = 1; (c) an = (d) a, = 40n-1- 3a,-2+2", a1 = 1, az 11. 6a,-1 - 9a,-2, a1 = 1, az = 9; %3! %3D %3D %3!
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- What is the general form of the solutions of a linear homogenous recurrence relation if its characteristic equation has the roots -1,-1,-1,2,2,5,5,7?This is a recurrence relations problem In Mayville, 90% of the existing dog licenses are reissued each year, and 1200 new licenses are issued. in 1995 there were 15,000 dog licenses issued. a. Write a difference equation and inital conditions describing the number of dog licenses Mayville will issue n years after 1995. b. How many dog licenses will Mayville issue in 2004? c. If the present trend continues, how many dog licenses can Mayville expect to issue after many years?A biologist has placed three strains of bacteria (denoted I, II, and III) in a test tube, where they will feed on three different food sources (A, B, and C). Each day 400 units of A, 500 units of B, and 600 units of C are placed in the test tube, and each bacterium consumes a certain number of units of each food per day, as sh own in Table . How many bacteria of each strain can coexist in the test tube and consume all of the food
- How many ways are there to arrange four men and five women in a row such that the men must be arranged in increasing order of their ages and the women must be arranged in increasing order of their ages?Suppose that you have a combination lock that uses letters instead of numbers for its combination, and that three letters make up the combination that will open the lock. If any of the 26 letters may show up in any of the three places of the combination (with no repeats allowed), how many combinations are possible with this lock?Suppose that you have a combination lock that uses letters instead of numbers for its combination, and that four letters make up the combination that will open the lock. If any of the 26 letters may show up in any of the four places of the combination (with repeats allowed), how many combinations are possible with this lock?
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