Create an R function pwfun(), which computes values of the piece-wise (mathematical) function pwfun defined in the following way: x < -1 .-15x51 Its graph is as follows. pwfun(c(-2, 0.5, 3)) 208 pwfun(x)= Your R function pwfun() should also accept x as a vector of arbitrary length and return vector of the same length with entries defined as values of the mathematical function pwfun, evaluated at the corresponding entries of vector x Here are some input vectors and what you should get as a corresponding output. pwfun (-1) 0 x= c(-3, -2, -1, 0, 1, 2, 3.2) pufun(x) 42000 39.24 -2x-2 0 x²-1

A sequence (bn)neNo is called strictly increasing if b₁ M. We can represent a sequence (bn) by a Python function that takes n as its argument (of type int) and returns bn (of type float). Write a function threshold_index that takes two arguments: The first one is a Python function representing a strictly increasing, divergent sequence. The second one is a threshold value M. The function threshold_index should return the smallest index n for which the sequence passes the threshold (i.e., bn ≥ M).

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ans in JS

1. Implement a helper function called rref pp (A, b) that applies Gaussian Elimination with partial pivoting to return the Reduced-Row Echelon Form of the augmented matrix formed from Matrix object A and Vec object b. The output must be of the type Matrix. 2. Implement the function solve pp(A, b) that uses rref pp (A, b) to solve the system A = b. The input A is of the type Matrix and b is of the type vec. o If the system has a unique solution, it returns the solution as a Vec object. o If the system has no solution, it returns None. o If the system has infinitely many solutions, it returns the number of free variables (int) in the solution. def _rref_pp(A, b): # todo pass def solve_pp(A, b): #todo pass Python

write a C++ function to compute the following (Set Theory)       a.   std::vector<int> intersection(std::vector<int>& a, std::vector<int>& b)       b.   std::vector<int> union(std::vector<int>& a, std::vector<int>& b)       c.  std::vector<int> abs_complement(std::vector<int>& u, std::vector<int>& a, std::vector<int>& b)        d. std::vector<int> relative_complement(std::vector<int>& u, std::vector<int>& a, std::vector<int>& b)  //a\b       e. std::vector<int> delta_diff(std::vector<int>& u, std::vector<int>& a, std::vector<int>& b)  //a = { x, y, z ... } void print(std::vector<int>& v, std::string& n) { std::vector<int>::iterator itr = std::begin(v); for (; itr != std::end(v); itr++) {    std::cout<<(*itr)<<std::endl; } }   int main(int avgc, char** avgs)  {  std::vector<int> u = {1, 2, 3,…

Return co-ordinate 1 from (vector 3 1 4 2). In Racket

3. 4. Given a directed acyclic graph G = (V, E) and two vertices s, te V, design an efficient algorithm that computes the number of different directed paths from s to t. Define the incidence matrix B of a directed graph with no self-loop to be an nxm matrix with rows indexed by vertices, column indexed by edges such that Bij = -1 1 0 if edge j leaves vertex i, if edge jenters vertex i, otherwise. Let BT be the transpose of matrix B. Find out what the entries of the n x n matrix BBT stand for.

Which of the following is the definition of a higher-order function?     func xs = sum (map (^2) xs)     func x = x * 2     func (x,y) = (y,x)     func (x:y:zs) = y     func f [x,y] = [f x, f y]

A sequence (bn)neN is called strictly increasing if b, M. We can represent a sequence (bn) by a Python function that takes n as its argument (of type int) and returns bn (of type float). Write a function threshold_index that takes two arguments: The first one is a Python function representing a strictly increasing, divergent sequence. The second one is a threshold value M. The function threshold_index should return the smallest index n for which the sequence passes the threshold (i.e., bn ≥ M).