Question

(10 pts) What is the general form of the solution of a linear homogeneous recurrence relation if its characteristic equation has roots 1, 1, 1,2,2,3? .(10 pts) You are a chief for an electric utility company. The employees in your section cut down trees, climb poles, and splice wire. You report that of the 128 employees in your department 10 cannot do any of the three (management trainees), 25 can cut trees and climb poles only, 31 can cut trees and splice wire, but not climb poles, 18 can do all three, 4 can cut trees only, 3 can splice wire, but cannot cut trees or climb poles, and 9 can do exactly one of the three. How many employees can do at least two of the three jobs mentioned? & (10pts) There are twelve signs of zodiac. How many people are needed to guarantee that at least three were born on the same day of the week and have the same zodiac sign? (10 pts) How many different combinations of pennies, nickels, dimes, quarters, and half dollars can a piggy bank contain if it has 20 coins in it? (10 pts) A student has three mangoes, two papayas, and two kiwi fruits. If a student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed?

Answer 1

@ Characteristic equation has root 11, 1, 2, 2, 3.. li repeated 3 times, 2 is repeated twice 1. General form of solution is an = A ( + Bn Litch? (1? + D (2) + En(2)+F(3)? an= A + Bn + Cn² + D2n + En an+F30 where A, B, C, D, E, F are arbitrary constants.