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    Basic Algebra

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    Problem 12

    Select the point which is in the feasible region of the system of inequalities: 4x + y < 8 2x + 5y < 18 x > 0, y > 0 A. (2,4) B. (-1,2) C. (1,3) D. (4,1)

    Denumerable and Induction

    1. Show that if A and > are denumerable disjoint sets then A u > is denumerable 2. Show that every set of cardinalty c contains a denumerable subset 3. Show by induction that 6 divides n^3 - n for all n in N

    Sum of consecutive odd integers

    If m and n are odd integers with n>1, given the sum of n consecutive odd integers, starting with m, is 18,079. Find all possible values of m and n.

    Lebesque measurable sets in R^n.

    Prove that lebesque measurable sets in R^n form sigma algebra. ( Please use basic definition when you talk about the lebesgue measurable sets in R^n). The def we have is: (k_1)^(m)={ -1/2 + m_i =< x_i =< 1/2+ m} m=(m_1,m_2,...,m_n) m belongs to z^d Now we say that A in R^n is Lebesque measurable set in R^n if

    Speed and Distance

    Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10 miles per hour faster than Leon, then how fast did each of them drive?

    Distance and Speed

    Janet drove 120 miles at x mph before 6:00 a.m. After 6:00 a.m., she increased her speed by 5 mph and drove 195 additional miles. Write a rational expression for her total traveling time. Evaluate the expression for x = 60.

    Prove that if A is a set of positive, finite Lebesgue measure

    A point x of a measurable subset A of the reals is called a density point if m( A intersection [x-h, x+h] ) / 2h goes to 1 as h goes to 0 where m is the Lebesgue measure. Prove that if A is a set of positive, finite Lebesgue measure, then almost every point of A is a density point. I would like to note that I can use

    Context-fee language

    Thank you for taking the time to look at my problem. I cannot make math symbols, thus, I will let ^ denote "raised to the power." For example, a^2 is a squared or a "raised to the power" of 2. Also, I will use the symbol * to denote multiplication. For example, 2*7=14. Okay, here is my problem: Show that the language L={ a

    Algebraic Structures, Inverses, Finite Group, Identity

    5. Let (A, *) be an algebraic structure, and suppose that A is associative, has an identity, e, and that a &#1028; A has an inverse. Show that if ax = ay, then x = y. 8. Let G be a finite group with identity e, and let . Show that there is an n &#1028; N with a^n = e (Hint: Consider the set {e, a, a2 , ..., am }, where m

    Galois Theory / Solvability by Radicals

    Show that 2x^5-10x+5 is irreducible over Q using Eisenstein's Criteria and show it is not solvable by radicals using typical results/theorems in Galois Theory/Solvability of Radicals in Galois Theory.

    Functions and Relations

    A football player attempts a field goal by kicking the football. The ball follows the path modelled by the equation h=-4.9t2(means t squared)+10t+3, where h is the height of the ball above the ground in metres, and t is the time sincethe ball was kicked in seconds. 1. Describe the path of the ball. 2. After how many sec