Derive Open Newton's Cotes Formula for n=6 ?

Derive Closed Newton-Cotes Formulas for n=5 and n=4 ?

Let A = 0 2 0

1 0 2

0 1 0 .

(a) Find the eigenvalues of A and bases of the corresponding eigenspaces.

(b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line.

(c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist.

(d) Write down explicitly a diagonalizing matrix S, and a diagonal matrix Λ such that S −1AS = Λ; A = SΛS −1 . or explain why A is not diagonalizable.

Calculate the half of the ratio of perimeter of regular apeirogon to the distance of the centre of gravity to the edges of this regular apeirogon, find the 1288. 1289. 1290. and 1291. decimal places.

Compute the projection of y = (1, 2, 2, 2, 1)  onto span (x1, x2) where

x1 =(1, 1, 1, 1, 1)   x2 =(4, 1, 0, 1, 4)

The inner product to use is the usual dot product. (This will compute a best-fitting function that is quadratic with no linear term, fitting to the data (−2, 1),(−1, 2),(0, 2),(1, 2),(2, 1).)

Define T: P2 → P2 by T(a0 + a1x + a2x2) = (−3a1 + 5a2) + (−4a0 + 4a1 − 10a2)x + 5a2x2. Find the eigenvalues. (Enter your answers from smallest to largest.) (λ1, λ2, λ3) = −2,5,6 Correct: Your answer is correct. Find the corresponding coordinate eigenvectors of T relative to the standard basis {1, x, x2}. x1 = −5,10,0 Incorrect: Your answer is incorrect. x2 = − 5 2​,5,1 Incorrect: Your answer is incorrect. x3 = − 1 2​,1,0 Incorrect: Your answer is incorrect.

Let A be a diagonalizable n × n matrix and let P be an invertible n × n matrix such that B = P−1AP is the diagonal form of A. Prove that Ak = PBkP−1, where k is a positive integer. Use the result above to find the indicated power of A. A = 6 0 −4 7 −1 −4 6 0 −4 , A5 A5 =

at time t=0, a particle is located at the point(4,8,7). it travels in a straight line to the point (7,1,6), has speed 7 at (4,8,7) and constant acceleration 3i-7j-k. Find an equation for the position vector r(t) of the particle at time

1. A company produces and sells two different products. The demand for each product is unlimited, but the company is constrained by cash availability and machine capacity. Each unit of the first and second product requires 3 and 4 machine hours, respectively. There are 20,000 machine hours available in the current production period. The production costs are $3 and $2 per unit of the first and second product, respectively. The selling prices of the first and second product are $6 and $5.40 per unit, respectively. The available cash is $4,000 and furthermore, 45% of the sales revenues from the first product and 30% from the second product will be made available to finance operations during the current period.
(a) Formulate an LP problem that maximizes the company’s net income subject to cash availability and machine capacity limitations.
(b) Solve the problem graphically to obtain an optimal solution.
(c) Suppose that the company could increase its suitable machine hours by 2,000 after spending $400 for certain repairs. Should the investment be made?

pleas solve all show all steps I Need it as notes no app plz

Apply the KKT conditions to determine whether or not the solution XT = (1,1,1) is optimal for the following problem:

minimize 2X1 + X2^3 + X3^2

subject to

2X1^2 + 2X2^2 + X3^2 >=4

X1, X2, X3 >=0

u'' + sinu = sinx (-1<x<1)

u(-1)=1, u'(1)=0

solve this boundary value problem.

Hello! I am stuck on the following question: Show that every simple subgroup of S_4 is abelian.