### Relation

Let R be the relation { (1,2), (1,3),(2,3),(2,4),(3,1)} and let S be the elation { (2,1),(3,1),(3,2),(4,2)}. find SoR

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Let R be the relation { (1,2), (1,3),(2,3),(2,4),(3,1)} and let S be the elation { (2,1),(3,1),(3,2),(4,2)}. find SoR

The following second order Differential Equations must be solved with the appropriate Infinite Series Method. You may verify DE with other method only after work is shown step by step using the infinite series methods. Problems Use appropriate infinite series method about x=0 to find solutions of the given DE. 1) xy"-

Hi, The general solution to 2a_{n+2} - 3a_{n+1} - 2a_n = 0 is a_n = A*2^n + B*(-1/2)^n I'm after the general solution for some variations on the above ... 2a_{n+2} - 3a_{n+1} - 2a_n = 36n 2a_{n+2} - 3a_{n+1} - 2a_n = 28 * 3^n 2a_{n+2} - 3a_{n+1} - 2a_n = 25 * 2^n

I need to find the general solution for the following recurrence relation but in a form that doesn't contain complex numbers. a_{n+2}+2a_{n+1}+5a_n = 0

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

Prove that "having the same homotopy type" is an equivalence relation on the set of topological spaces.

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

4. In noncommutative algebra, the term monomial refers to any arrangement of a sequence of variables from a set. For example, in a noncommutative algebraic structure on a set of four variables, {x,y,z,w} , examples of monomials of length 3 are xxx,xyx,xxy,zwy,wzx........ a) Write a generating function for the number of monom

1) Find and solve a recurrence relation for the number of n-digit ternary sequences with no consecutive digits being equal. 2) Find and solve a recurrence relation for the number of infinite regions formed by n infinite lines drawn in the plane so that each pair of lines intersects at a different point. 3) Find and solve a

Consider the recurrence relation . Show that the general solution is . Show that the solution with starting values and corresponds to and . Please see the attached file for the fully formatted problems.

See attached file for full problem description.

_______ Y =√ X - 2 _________ Y = √ X + 4 ___ Y= √ 2X _______ Y= √ 2X - 1

Find and prove a closed form for the recursion X_0 = 1, X_n = 3X_(n-1) - 1

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

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

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

5b. Describe the equivalence classes for the following relations on N. x~y iif x mod 2 = y mod 2 and x mod 4 = y mod 4

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

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

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.

Prove that the Fibonacci sequence can be obtained by the recurrence relationship. See attached file for full problem description.

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

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).

An = 1/2n. Write the recursion formula for this series?

Suppose a sequence satisfies the given recurrence relation and initial conditions. Find an explicit formula for the sequence s(subk)=-4s(subk-1)-4S(subk-2), for all integers k>or equal to 2 s(sub0)=0,S(sub1)=-1