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- Create a VI that would plot the following functions into a chart and a graph: the exponential function y = ex , the logarithmic function y = ln x, hyperbolic cosine function y = cosh x and the cosine function y = cos x for 0 ≤ x ≤ 5. Choose appropriate spacing to ensure smooth plot. Choose the appropriate scaling for the x and y axes so that the user will have an idea on how the function behaves as x gets larger. Make sure also that the user will be able to discern which plot is which. Finally, choose which is the better tool to plot such functions so that the user will be able to use the plots for better understanding of the behavior of the function. (LabVIEW programming)arrow_forwardLet l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂arrow_forwardWe now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) 1) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Doing the corresponding numerical simulations show what happens with the increase of the difference between the frequencies of the two waves and vice versa.arrow_forward
- Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solutions including original diagram for part a!arrow_forwardAnswer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solution!arrow_forwardWe have been working extensively with the predicate "eventually greater than" defined on pairs of functions f of g. Which of the following is equivalent to f(x) is not eventually greater than g(x)? (Select all that apply) Group of answer choices ¬((∃x0)(∀x)(x>x0→f(x)>g(x))) ((∃x0)(∀x)(x>x0→f(x)≤g(x))) (∀x)(∃x0)(x0>x→f(x0)≤g(x0)) (∀x)(∃x0)(x0>x→f(x0)≤g(x0))arrow_forward
- Please answer the following question in depth with full detail. Suppose that we are given an admissible heuristic function h. Consider the following function: 1-h'(n) = h(n) if n is the initial state s. 2-h'(n) = max{h(n),h'(n')−c(n',n)} where n' is the predecessor node of n. where c(n',n) min_a c(n',a,n). Prove that h' is consistent.arrow_forwardLet A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6, 7} and C = {a, b, c, d, e} 17. Give an example of f: A -> B, g: B -> C such that (g o f) is 1-1 but g is not 1-1.arrow_forwardLet A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6, 7} and C = {a, b, c, d, e} 15. Give an example of f: A -> B that is not 1-1.arrow_forward
- Let l be a line in the x-y plane. If l is a vertical line, its equation is x 5a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y 5mx 1b, where b is the y-intercept. If l passes through the point (x0, y0,), the equation of l can be written as y 2y0 5m(x 2x0 ). If (x1, y1) and (x2, y2) are two points in the x-y plane and x1 ≠ x2, the slope of line passing through these points is m 5(y2 2y1 )/(x2 2x1 ). Write a program that prompts the user two points in the x-y plane. The program outputs the equation of the line and uses if statements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If l is a non-vertical line, output its equation in the form y 5mx 1b.arrow_forwardGiven functions f:R → R and g: R → R. Suppose that go f turns out as go f(x) = (x2 + 7]. Identify the g(x) and f(x) that produce the go f(x) as stated. Also, plot g(x) and f(x).arrow_forwardWrite a function linear_independence that takes a collection of vectors with integer entries (each written as a list), and returns True if this collection of vectors is linearly independent, and False otherwise. Examples: linear_independence([1,2]) should return True. linear_independence([1,3,7],[2,8,3],[7,8,1]) should returnTrue. linear_independence([1,3,7],[2,8,3],[7,8,1],[1,2,3]) should return False.arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole