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a) Determine the irreducibility of x20-11 over Q(set of rationals), and use it to prove or disprove that the ideal <x20-11> is a maximal ideal of Q[x].
b) Construct an integral domain R and an element a in R such that a is irreducible but not prime in R.
c) Suppose that R is a principal ideal domain and a in R is irreducible. If a does not divide b in R, prove that a and b are relatively prime.
d) Suppose p in N(set of naturals) is a prime number. Show that every element a in Zp has a p-th root, i.e. there is b in Zp with a=bp.
armando has an a average for his test scores. his test percentages so far are 96 92 and 97. what is the mean of the
Suppose a culture of bacteria starts with 5000 bacteria. After one hour, the count is 6000. Find an exponential equation that models the number of bacteria in hours. Keep at least 4 decimal places in your formula for rounded values. Find the doubling..
Q1. What is sampling error? Could the value of the sampling error be zero? If it were zero, what would this mean? Q2. List the reasons for sampling. Give an example of each reason for sampling.
Consider the map Φ : (Z, +) →(Zn, + (mod n)) given by Φ(t) ≡ t (mod n). State the first isomorphism theorem and apply it to the map Φ
What can you tell about the algebraic and geometric multiplicities?
a trendy garment receives orders from three boutiques. the first boutique orders 25 jackets 75 shirts 75 pairs of
Write the following as an algebraic expression using x as the variable : the sum of a number and -8. Write the following as an algebraic expression using x as the variable: Five more than the product of 7 and a number.
The area of a rectangular athletic field is represented by the expression 12y^3+48y^2+24y square meters. Write an algebraic expression to represent one possible set of dimensions (in the sense "length times width") of the athletic field.
Let and let be the linear transformation given by find the matrix A of T with respect to the standard basis of both V and W.
Determine the corresponding z -transform G(z) and the characteristic equation for this system. Using the bilinear transformation and Routh's Stability Criterion, determine the range of K for stability when the sampling time T = 0.25 s.
Could you explain me the easiest steps needed to prove the Holder inequality for L^p spaces?
Isolating the natural logarithm
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