### Find Irreducible Polynomial

Find an irreducible polynomial defining the extension Q(3^1/2, 5^1/2).

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Find an irreducible polynomial defining the extension Q(3^1/2, 5^1/2).

Let K be obtained as a field Q(alpha) where alpha is a root of P(x) = x3 −3. Find an irreducible polynomial which defines the splitting field of P(x).

Please see the attached file for the fully formatted problem. Show the existence of an extension of Fq of order l for any prime l.

Please see the attached file for the fully formatted problem. (y2 + y - 12)/(y3 +9y2 + 20y)/[(y2-9)/(y2+3y2)]

6) Suppose we have a building with a floor shaped like an isosceles right triangle. The two sides adjacent to the right triangle have length 100 feet. Think of the right angle being at the origin, and other two corners at (100, 0) and (0, 100). The overhead crane is located at the origin and needs to travel to a point (X, Y), w

At Very Long Hotel in Florida, there are n rooms located along a very long corridor and numbered consecutively from 1 to n. One night after a party, n people, who have been likewise numbered from 1 to n, arrived at this hotel and proceeded as follows: Guest 1 opened all the doors. Then Guest 2 closed every second door beginnin

Let n be a natural number, and let f(x) = x^n for all x are members of R. 1) If n is even, then f is strictly increasing hence one-to-one, on [0,infinity) and f([0,infinity)) = [0,infinity). 2) If n is odd, then f is strictly increasing, hence one-to-one, on R and f(R) = R. "This needs to be a proof by induction, provin

Describe all nonisomorphic central extensions of Z_n by Z_2 x Z_2 meaning central group extensions of the following form 1 --> Z_n --> G --> Z_2 x Z_2 --> 1 Meaning, determine those nonisomorphic groups G that can be described by such an extension. Please also explain how you came up with the answer.

Please see the attached file for the fully formatted problems. Problem 3: This problem itself is directly creating perceptual curiosity and at the cognitive level it is against what is known in the mathematics. The problem is: 13+23+33+.... +n3 = (1+2+3+...+n) 2 Visual representation of problem: Sum of the cubes

You have three thousand bananas that you have to get to a destination 1000 miles away. You can only carry 1000 bananas at a time. You also must eat 1 banana per mile for energy. Assuming you design your trip as efficiently as possible, how many bananas will you have left when you arrive at the destination? (apparently someon

If we assign number values to letters in the following way: A = 26, B = 25, C = 24 and so on until Y = 2 and Z =1, spell a word such that the product of its letters is as close to a million as possible. Explain how you went about solving this problem.

As provided by E. Galua theory the general algebraic equations for a polynomial of fourth order ax^4 + bx^3 + cx^2 + dx + f=0 (*) is the maximum order type of algebraic equations the solution to which one can write down in radical expressions. Among all the equations of fourth

Please see the attached file for the fully formatted problems. 1) Have you ever seen the written form of the Sanskrit language? If so, you probably are amazed at how different this ancient language from India looks from ours. Some English words, however, are based on Sanskrit. For example, cup comes from the Sanskrit work kup

What is the remainder when the product of one hundred 5's is divided by 7? Please be detailed in your response.

During the census, a man told the census-taker that he had three children. When asked their ages he replied, " The product of their ages is 72. The sum of their ages is my house number." The census taker turned around and ran outside to look at the house number displayed over the door. He then re-entered the house and said, "

Three people play a game in which one person loses and two people win each game. The one who loses must double the amount of money that each of the other players has at that time. The three players agree to play three games. At the end of the three games, each player has lost one game and each has $8. What was the original st

Two swimmers start at opposite ends of a pool 89 feet long. One person swims at the rate of 19 feet per minute and the other swims at a rate of 53 feet per minute. How many times will they meet in 33 minutes? Plese try to give a detailed response as my answer is not as important as the thought processes that I must understa

Please see the attached file for the fully formatted problems. Find a solution in the form of a power series for the equation y" - 2*x*y' = 0 (ie find 2 linearly independent solutions y1(x) and y2(x)). After doing that, note that the equation can also be solved directly by integration: y"/y' = 2x ln(y') = x^2 +

PART ONE: solve: (3n^5 w)^2 /(n^3 w)^0 A) 0 B) 9n^7w C) 6n^4w D) 9n^10w^2 PART TWO: solve: 9c^7 w^-4 (-d^2)/(15c^3 w^6 (-d)^2) A) 3c^4d^2/5w^10 B) 3c^4/5w^2 C) 3c^4/5w^10 D) -3c^4/5w^10 PART THREE: solve: 5m^-3 /6^-1 m^-2 A) -5m/6 B) 30/m C) 30m D) -5/6m PART

Please see the attached file for the fully formatted problem. Solve the algebraic equation. (x-6)^1/2 = (x+9)^1/2 - 3

Suppose the series ak (the k is subscript) converges absolutely and that the series bk is bounded. Show that the series ak*bk converges absolutely.

Factor completely 2X^2 + 21 = -17X

For which integers c, 0<=c<=1001, does the congruence 154x=c(mod1001) have a solution? When there are solutions how many incongruent solutions are there?

How do I prove the fundamental theorem of algebra by using Rouche's theorem?

PROLOG Due 7/10 NOTE: For your homework, you are not allowed to use the builtin predicate definitions. If, for example, you want to use member/2, create you own version called mymember/2 (or something). Same for append, reverse, sort, and many others.You may use any builtin numeric operators, 'is', the '[' ']' brackets f

Complete the algebra questions in attachment 1. Find the domain of the given function. 2. Reduce the given expression to lowest terms. 3. Find the solution set of the given equation. Match your result to the correct answer below. 4. Convert the given expression into an equivalent expression that has the indicated denominator

Please see the attached file for the fully formatted problems. 1: Use the Euclidean Algorithm to find the Highest Common Factor of 1176 and 1960. 2: Use the rules of natural deduction to prove ((A --> (B -->C)) -->((A B)--> C)). [12 marks] 3: Use the rules of natural deduction to prove (A (B U C)) ((A B) C) [14 ma

Please see the attached file for the fully formatted problem(s). Practice Problems Directions: Show work to support your final result. Examples requiring mathematical work to support the result must be included, if final answer is correct but supporting work is missing. Examples that require a graph DO NOT need the gr

Solve any 6 equations/inequalities by the indicated method. If no method is indicated then you can solve either algebraically or graphically. Solution by graphing requires a sketch of the graph or a written description of the graph and where the solution lies. Solve any 6 equations/inequalities by the indicated method. If

I have a formula, known as the Bass Curve Formula, that I would like rearranged. The formula generates an S curve that initially grows slowly, then accelerates before slowing down and plateauing. (See example) I would like the formula to be rearranged to find a variable (p). Please find the attached file for a detailed e