(1 point) (3 Marks] Note that 0 € N. Give a recursive function f:N → N...
(1 point) [3 Marks] Note that 0 € N. Give a recursive function f:N + N that represents the sequence ao, 21, 22, az... if an = 10n + 1.
(1 point) [3 Marks] Note that 0 € N. Give a recursive function f: N N that represents the sequence ao, 21, 22, 23... if an= 5n + 1. A. I am finished this question
Note that 0 EN Give a recursive function f:N → N that represents the sequence ao, 21, 22, 23... if an 10n +1.
Suppose f:N → N satisfies the recurrence f(n+1) = f(n) 7. Note that this is not enough information to define the function, since we don't have an initial condition. For each of the initial conditions below, find the value of f(7). a. f(0) = 1. $(7) = b. f(0) = 5. f(7) = c. f(0) = 19. f(7) = d. f(0) = 249. f(7) =
Problem 5. (1 point) [5 Marks] Consider the following integer n = 516734400 = 2 · 37 · 52 · 72 · 133. a) How many positive divisors does n have? b) How many of the positive divisors of n are perfect cubes? That is, the number can be written as (k)3 for some k e Z. c) How many of the positive divisors of n are relatively prime with 21? A. I am finished this question
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
1 1 point Consider the following algorithm for factoring an integer N provided as input (in binary): For i = 2 to [VN.17 i divides N, then output (i, N/). Which of the following statements is true? This algorithm is correct, but it runs in exponential time. This algorithm is not correct, because it will sometimes fail to find a factorization of Neven if N is composite This algorithm runs in sub-linear time, and always factors N it Nis composite...
22 - 1 point Find a polar equation of the hyperbola ()? - G =1. Note: use t for 0. Submit I am finished
The Fibonnaci sequence is a recursive sequence defined as: f0 = 1, f1 = 1, and fn = fn−1 + fn−2 for n > 1 So the first few terms are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, . . .. Write a function/procedure/algorithm that computes the sum of all even-valued Fibonnaci terms less than or equal to some positive integer k. For example the sum of all even-valued Fibonnaci terms less than or equal to 40...
Give a recursive definition of the sequence {an}, n = 1, 2, 3,... if an = n2 커-1, an-an-1+2n, for all n>1 어=1, an = an-1+2n-1, for all n21 an = an-1+2n-1. for all n21 gel, an=an-1+2n-1, for all n>1 -1, an- an-1+2n-1, for all n2o