Let w(t) be a blended piecewise- linear trajectory through the points {wo, w', w} with segment traversal times of {T} and a blend transition time of AT. Then the blend acceleration a is as in Prop. 4-7-2, and the complete trajectory is: w(t) wo + = a - Aw' T₁ 0≤1 ≤T-AT T₁ + AT)² + Aw'(1-T) T₁ + w₁ T₁ AT <
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- A fixed beam is subjected to a uniformly-distributed load with an intensity of f = 10 N/mm length of L = 200 mm. Now determine the support reaction forces, internal shear forces and moments, then plot its internal shear force and moment diagram. f[N/m] L 1. Define the paramters, use L and f as the variables y XWe have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, X2, ..., Xn,..., XN. Each interval is Ax = (b – a)/N. The Simpon numerical integration rule is derived as: N-2 Li f(x)dx = * f(x0) + 4 (2n odd f(xn)) + 2 ( En=2,n even N-1 f(x,) + f(xn)] . Now complete the Python function InterageSimpson(N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f (x) = 2x³ (Already defined, don't change it). In [ ]: # Complete the function given the variables N,a,b and return the value as "TotalArea". # Don't change the predefined content, only fill your code in the region "YOUR CODE" from math import * def InterageSimpson (N, a, b): # n is…We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, x2,.. Xn,..., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x) dx N-1 Ax [ƒ(x0) + 4 (Σ1,n odd f(xn)) ƒ(x₂)) + f(xx)]. N-2 + 2 (n=2,n even Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is ƒ(x) = 2x³ (Already defined in the function, no need to change).
- We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b]. Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1,x2,..., X., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x)dx ≈ [ƒ(x0) + 4 (EN-1,n odd S(x)) + 2 (Σ2²n even f(x)) + f(XN)]. Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f(x) = 2x³ (Already defined in the function, no need to change). *Complete the function given the variables N, a,b and return the value as "TotalArea"." "Don't change the predefined content' only fill your code in the region *YOUR CODE"" from math import * def InterageSimpson (N, a,…A = ? y = ? The critical point in barycentric coordinates xb and xcPlease explain how that is simplified to Y=A, using Karnaugh Maps with 1 and 0 not the other solution that was just submitted
- Fully developed flow moving a 40 cm diameter pipe has the following velocity profile: Radius r, cm 0.02.55.07.510.0 12.5 15.0 17.5 20.0 Velocity v, m/s 0.914 0.890 0.847 0.795 0.719 0.543 0.427 0.204 0 Find the volumetric flow rate Q integrate from 0 to R using the relationship Q = [_0^R_ 2rtrvdr. Where r is the radial axis of the pipe, R is the radius of the pipe and v is the velocity. Solve the problem using two steps. Fit a polynomial curve to the velocity data using polyfit. Integrate the equation using int.Suppose that we want to solve the system Ax = b, where <image> and b = (1,7,16,14)T, Do three iterations of SOR for Problem 1, using ꙍ= 1.05. problem 1 results x(1) = (0.25, 1.4, 2.67, 3.5 ) x(2)=(-0.1, 0.816, 1.85, 2.77) x(3)= (0.046, 0.35, 2.07, 2.833)Let i, j, w, x ∈ Za with i, j different from each other and w, x different from each other. When an invertible function f : Za → Za is chosen at random, what is Pr[f(j) = x | f(i) = w]?
- Simplify the following functions using K-maps, and then derive the corresponding simplified Boolean expressions. Note that d stands for don't-care cases. a) F(w,x,y,z) = Σ(0,2,8,10, 12, 13, 14) b) F(w,x,y,z) = (0,2,3,5, 7, 8, 10, 11, 14, 15) c) F(A,B,C,D) = [[(1,3,6,9,11,12,14) d) F(x,y,z) = (0,4,5,6) and d (x, y, z) = Σ(2,3,7)13Simplify the following Boolean function using K-map ? F(X,Y,Z)=DTTM(0,1,2,4)