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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- Use kernel trick and find the equation for hyperplane using nonlinear SVM. Positive Points: ((1,0), (3,0), (5,0)} Negative Points: {(0,0), (2,0), (4,0), (6,0)%. Plot the point before and after the transformation.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 xc
- Simplify the boolean function using carno map in it.Please explain how that is simplified to Y=A, using Karnaugh Maps with 1 and 0 not the other solution that was just submittedIn Sammon mapping, if the mapping is linear, namely, g(x|W) = WTx, how can W that minimizes the Sammon stress be calculated?
- use a CAS to perform the following steps for the given curve over the closed interval. a. Plot the curve together with the polygonal path approximations for n = 2, 4, 8 partition points over the interval. b. Find the corresponding approximation to the length of the curve by summing the lengths of the line segments. c. Evaluate the length of the curve using an integral. Compare your approximations for n = 2, 4, 8 with the actual length given by the integral. How does the actual length compare with the approximations as n increases? Explain your answer. x = 2t^3 - 16t^2 + 25t + 5, y = t^2 + t - 3, 0 … t … 6Let (X, Y) - Uniform(D) with DC R2 being a disc contered at the point (a, b) (s00 the Figure below). Dofine V(x-a)2 +(Y-6)2 Out of the four random variables X, Y,0, R. find a pair which Y-by = arctan and R is independent. (,4) O (X,Y) O (X, R) O (X, e) O (R,Y) o (e,Y) O (R,e) 1. Out of the four random variables X,Y, R, 0. find a pair which is independent. True O False 2. The random variables X, Y aro uncorrolatod.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.