A field F is said to be perfect if every polynomial
over F is separable. Equivalently,
every algebraic extension of F is separable. Thus fields of
characteristic zero and
finite fields are perfect. Show that if F has prime characteristic p,
then F is perfect
if and only if every element of F is the pth power of some element
of F. For short we
write F = F p.
In: Advanced Math
prove that a translation is an isometry
"i want the prove by using a parallelogram and proving that the two
side are congruent please"
In: Advanced Math
Multivariate analysis
Using the data provided, perform the following analysis:
Interpret the results by answering the following questions:
sales^ = (intercept) + (coefficient)× marketing + (coefficient)× price
Total sales | Marketing | Price |
£ 1,500.00 | £ 330.00 | £ 3.50 |
£ 1,354.00 | £ 270.00 | £ 3.75 |
£ 1,489.00 | £ 320.00 | £ 3.50 |
£ 1,347.00 | £ 280.00 | £ 3.90 |
£ 1,321.00 | £ 260.00 | £ 4.00 |
£ 1,245.00 | £ 240.00 | £ 4.20 |
£ 1,589.00 | £ 325.00 | £ 3.50 |
£ 1,632.00 | £ 340.00 | £ 3.30 |
£ 1,485.00 | £ 320.00 | £ 3.40 |
£ 1,420.00 | £ 300.00 | £ 3.70 |
In: Advanced Math
What is the last digit of 123456789012345678×609 in base 6. Don’t try to compute the product.
In: Advanced Math
30r+45d
10r+15d≤1800
20r+25d≤2500
6r+15d≤1500
s.t.
a) Use the Graphical Solution Method to solve the linear
programming problem (label all functions, corner point points, and
axis).
r≥50
2d-1r ≥0
r,d≥0 or all variables non-negative
In: Advanced Math
7. Let E be a finite extension of the field F of prime
characteristic p. Show that the
extension is separable if and only if E = F(Ep).
In: Advanced Math
let E be a finite extension of a field F of prime
characteristic p, and let K = F(Ep)
be the subfield of E obtained from F by adjoining the pth powers of
all elements of
E. Show that F(Ep) consists of all finite linear combinations of
elements in Ep with
coefficients in F.
In: Advanced Math
Let A = {r belongs to Q : e < r < pi} show that A is closed and bounded but not compact
In: Advanced Math
Let α ∈ C be a root of x^2 + x + 1 ∈ Q[x]. For γ = 3 + 2α ∈ Q(α), find γ^ −1 as an element of Q(α).
Let a = 3 + 2(2^(1/3)) + 4^(1/3) and b = 1 + 5(4)^(1/3) belong to Q( 2^(1/3)). Calculate a · b and a −1 as elements of Q( 2^(1/3)).
In: Advanced Math
The data set cherry.csv, from Hand et al. (1994), contains measurements of diameter (inches), height (feet), and timber volume (cubic feet) for a sample of 31 black cherry trees. Diameter and height of trees are easily measured, but volume is more difficult to measure.
(i) Suppose that these trees are a SRS from a forest of N = 2967 trees and that the sum of the diameters for all trees in the forest is tx = 41835 inches. Use ratio estimation to estimate the total volume for all trees in the forest. Give a 95% CI.
(ii) Estimate the average timber volume and construct the 95% CI.
"Diam","Height","Volume" 8.3,70,10.3 8.6,65,10.3 8.8,63,10.2 10.5,72,16.4 10.7,81,18.8 10.8,83,19.7 11,66,15.6 11,75,18.2 11.1,80,22.6 11.2,75,19.9 11.3,79,24.2 11.4,76,21 11.4,76,21.4 11.7,69,21.3 12,75,19.1 12.9,74,22.2 12.9,85,33.8 13.3,86,27.4 13.7,71,25.7 13.8,64,24.9 14,78,34.5 14.2,80,31.7 14.5,74,36.3 16,72,38.3 16.3,77,42.6 17.3,81,55.4 17.5,82,55.7 17.9,80,58.3 18,80,51.5 18,80,51 20.6,87,77
In: Advanced Math
Let W be a subspace of Rn. Prove that W⊥ is also a subspace of Rn.
In: Advanced Math
Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 2 −2 5 0 3 −2 0 −1 2 (a) the characteristic equation (b) the eigenvalues (Enter your answers from smallest to largest.) (λ1, λ2, λ3) = the corresponding eigenvectors x1 = x2 = x3 =
In: Advanced Math
Find all the six roots of z = 16−16 sqrt (3i).
In: Advanced Math
find a linear combination for gcd(259,313). use extended euclidean algorithm.
what is inverse of 259 in z subscript 313?
what is inverse of 313 in z subscript 259?
In: Advanced Math
In: Advanced Math