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- Let f and g be functions from the positive integers to the positive integers defined by the equations f(x) = 3x + 1, g(x) = x2 + 2, h(x) = 7x - 3 Find the compositions a) g°h (x) b) g° f (x)arrow_forwardCompute the following values of ψ(X, B), the number of B-smooth numbers between 2 and X. (c) ψ(50, 7)arrow_forwardQ3 A: Simplify the following Boolean functions, using Karnaugh maps: F (xy, z) Σ (0,1,4,5)arrow_forward
- Select the correct answer for each given pair of functions f(n) and g(n)arrow_forward5. For each of the following functions over the positive integers, represented inunary, give the transition diagram of a TM that computes the function. (a). f(x) = ((x+1) mod 2) + 1 (b). g(x) — За +4arrow_forward10. Show that a Boolean function can be represented as a Boolean product of maxterms. This representation is called the product-of-sums expansion or conjunctive normal form of the function. [Hint: Include one max- term in this product for each combination of the variables where the function has the value 0.]arrow_forward
- cos h x thatarrow_forwardLet f(n) and g(n) be asymptotically positive functions. In the space provided, prove or disprove the following statement using rigorous mathematical argumentationarrow_forwardts) The phase plot for an ODE - f(N) is shown below. (a) Which of these could be a plat of solutions y vs z comresponding to this CDE? A. B. C. D. You can cilck the graphs above to enierge them. OA. A OB. B OC. C OD. D (D) One equilibrium solution af this ODE is y which is chogse and another equilbrium solution of this CDE is y - which is choase (C) For which of the following value(s) of the initial condtion y(0) does the solution g(z) converge as z 00? Select all that apply DA. 0) - 3 OB. 0) - 3.5 OC. p(0) - 2 OD. (0) - -1arrow_forward
- Please answer a. and b.arrow_forwardSolve d, e and f.arrow_forwardQ1/The pressure drop in pascals (Pa) for a fluid flowing in a pipe with a sudden decrease in diameter can be determined based on the loss of head equation given below: h = 24-11 2g Area A Area A Area A Where: V₂ is the velocity in position 2 (m/s), g: is acceleration due to gravity = 9.81 m/s², A₁ and A₂ are the cross-sectional areas of the tube in position 1 and 2 respectively. A==d² Where: d is the diameter (m). Write a program in a script file that calculates the head loss. When the script file is executed, it requests the user to input the velocity (V₂) in m/s and values of diameters (d, and d₂). The program displays the inputted value of v followed by a table with the values of diameters in the first and second columns and the corresponding values of h, in the third column. 2 2arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
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