Explore BrainMass
Share

Recurrence Relation

Recursions, Recurrence Relations, Difference Equations

1. Solve xn=axn-1+b when a=1. 2. An isotope of carbon called carbon-14 (14C) is used to establish the age of artifacts and fossils. It decays so that every 5000 years an amount of 14C is reduced to 54.44256% of its initial valued A archaeologist finds a fossil that contains 16% of the amount of 14C it contained when it was al

Recurrence Relation : Compound Interest

1. Pauline takes a loan of S dollars at an interest rate of r percent per month, compounded monthly. She plans to repay the loan in T equal monthly installments of P dollars each. a) Let a(subscript n) denote the amount Pauline owes on the loan after n months. Write a recurrence relation for a (subscript n). b) Solve the rec

R-Digit Ternary Sequences

How many r-digit ternary sequences are there in which: A) No digit occurs exactly twice? B) 0 and 1 each appear a positive even number of times? See the attached file.

Prove theta Relation : Reflexive, Symmetric and Transitive

Prove that theta is a reflexive, symmetric, and transitive relation; that is for all f, g, h: N to N, a. f belongs to theta f; b. f belongs to theta g then g belongs to theta f; c. f belongs to theta g and g belongs to theta h then f belongs to theta h;

Probability : Mean, Standard Deviation and Recurrence Relation

In order to test a vaccine, we have to find patients with a certain blood type, that is found in 20% of the population. Model W, the number of people sampled until we have found one with thhis blood type; X, the number sampled to find four with the blood type; and Y, the number with this blood type among 20 people. Find the mean

Domain and Range of a Relation

1. Find the domain and range of the relation {(x,y)&#9474;5x < -5} 2. Find the domain of the relation A={(x,y)&#9474;x^2+y^2=4}

Joint Mass Function, Forming a Triangle and Recurrence Relation

Suppose the joint mass function of X and Y, the numbers of goals scored by home and away teams in a soccer league is as shown in the below table... Another way in which a stick might be broken "at random" is to independently Select random points in each of the two halves. What would be the chance of the three pieces forming

Curls : Green's Theorem

When I write A_n it means A "sub" n. a) Define A_n= integral from 2pi to 0 of (Cos(theta))^(2n).d(theta) Proove the recurrence formula(*): A_n=(2n-1)/(2n)*A_(n-1) by writing Green's thorem for vector field F=x^(2n-1)j in the unit disc x^2+y^2<1 and evaluating each of the integrals sepa

Solving a Recurrence Relation

Solve the following recurrence relation: a(n) = a(n-1) + 3(n-1), a(0) = 1 I know this should not be a difficult problem, but my main problem is in solving the problem when the coefficient of the a(n-1) term is 1. Also, when a summation is in the solution, I do not understand how to convert from a summation to a C(n,k)

Solving recurrence relations.

Find and solve a recurrence relation for the number of ways to make a pile of n chips using red, white, and blue chips and such that no two red chips are together.

Relations: Properties and Equivalence Classes

Please see the attached file for the fully formatted problem. Exercise 5 (4p) R is the relation defined on Z ts follows: for all m,n E Z, m R n <=>4|(m-n) a. Determine whether the relaition is reflexive. b. Determine whether the relation is symmetric. c. Determine whether the relation is transitive. d. In case the relat

Equivalence Class Relations

Let P, P' be equivalence relations on a set A. Let n, n' be the number of equivalence classes of p, p', respectively. A) define an equivalence relation p'' as follows: xp''y <=> (xpy) and (xp'y) what is the least number of equivalence classes of p''? What is the greatest number of equivalence classes of p''? B)defin

Prove recurrence relationship of Catalan Numbers.

Prove recurrence relationship of Catalan Numbers. Question: Let n be a non-negative integer. The number, x[n], of topologically distinct binary trees with n nodes can be shown to satisfy the following recurrence (x[0] = 1): See attached file for full problem description.

Equivalence Relations and Class

Verify that each of the following are equivalence relations on the plane R^2 (where R are real numbers) and describe the equivalence classes geometrically. 1) (x1,y1)R(x2,y2) if and only if x1 = x2 2) (x1,y1)R(x2,y2) if and only if x1 + y1 = x2+y2 3) (x1,y1)R(x2,y2) if and only if x1^2 + y1^2 = x2^2 + y2^2.

Fibonacci sequence in closed form

Prove that Fn can be expressed by: Fn=[(a^n-b^n)/(a-b)] for n=1,2,3... ~: Set Gn=[(a^n-b^n)/(a-b)] and show that Gn satisfies the recurrence formula {G(n+1) = Gn + G(n-1) for n=2,3,4...} and don't forget that a and b satisfy the equation x^2-x-1=0. a and b are the roots of x^2-x-1=0, which are (1+sqrt5)/2 and (1-sqrt5)/2

Discrete Structures

1. Consider the sequence of triangles Ti, i >= 2: T2 is simply a triangle sitting upright, on its base. T3 is T2, except that an additional straight line is drawn from the upper vertex, down to somewhere on the base. For each Ti+1, one more line is added to triangle Ti (such that each line meets the base at a different point).