Quantitative Methods Answers

the position of f(x) of a particle moving in a line at various times xk is given in the following table. estimate the velocity and acceleration of the particle at x =1.2. f(1.0)=2.72, f(1.2)=3.32, f(1.4)=4.06, f(1.6)=4.96, f(1.8)=6.05, f(2. 0)=7.39, f(2.2)=9.02.

determine the constants a, b, c in the differentiation formula y '' (x0) =ay(x0-h) +by(x0) +cy(x0 +h). so that the method of the highest possible order and the error term of the method.

using the classical R-K method of O(h4) calculate approximate solution of the IVP y'=1-x+4y, y(0) =1 at x=0.6, taking h=0.1 and 0.2. use extrapolation technique to improve the accuracy.

for the linear system of equations [1 2 - 2,1 1 1, 2 2 1][x y z] =[1 3 5] set up the gauss - jacobi and gauss - seidel iteration schemes in matrix form. also check the convergence of the two schemes.

find the dominant eigenvalue and the corresponding eigenvector for the matrix A =[-4 14 0, - 5 13 0, - 1 0 2]using five itrations of the power method and taking y(0)=[1 1 1] as the initial vector.

find the inverse of the matrix A =[1 - 1 1, 1 - 2 4, 1 2 2] by gauss Jordan method.

estimate the eigenvalues of the matrix [1 - 2 3] [6 - 13 18] [4 - 10 14] using the Gershgorin bounds.draw a rough sketch of the region where the eigenvalues lie

what is the identity element in multiplication?

An automobile dealership uses CODE = 1 for new automobiles, CODE = 2 for used automobiles, and CODE = 3 for separate accessories. A salesman’s commissions are as follows: on new automobile, 3% of the selling price but a maximum of $300; on used automobile, 5% of the selling price but with a minimum of $75; on accessories, 6% of selling price.

1. Draw a flowchart that inputs CODE and PRICE and outputs COMMISSION.
2. Write a pseudocode programme that inputs CODE and PRICE and outputs COMMISSION.