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    Basic Algebra

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    Description of Abelian group

    Modern Algebra Group Theory (VII) To prove that if G is an abelian group, then for all a,b belongs to G and all integers n, (a.b)^n=a^n.b^n.

    Polynomial From Finitely Many Points on the Polynomial

    Alice: "I'm thinking of a polynomial f(x) with non-negative integer coefficients. Can you tell which one?" Bob: "Well, I need some information." Alice: "You can pick any real number r and I'll tell you f(r). Um....that is, I'll tell you finitely many digits of f(r) - but as many as you want." Bob: "Gee - just one value

    Sample problem set

    --- 1. Consider the following market demand and asymmetric cost functions for the airplane production industry. Market Demand is: P=200- (qA + qB) Cost Function for Boeing: C(qB) = 40 qB Cost Function for Airbus: C(qA) = 30 qA a.) Assume that the two act according to the Cournot mo

    Graphs and Functions : Asymptotes, X- and Y-Intercepts

    1. graph f(x) = + 5x+ 4 be sure to label all the asymptotes and to list the domain the x and y- intercept 2. f(x) = +3, x - sketch the graph and use the graph to determine whether the function is one to one -if the function is one to one find a formula the inverse 3. In ch

    Quadratic Equation Application Word Problems : Minimizing Cost

    If a manufacturer of lighting fixtures has a daily production cost of (x)=800-10x+0.25x^2 where c is the total cost in dollars and x is the number of units produced. - How many fixtures, x, should be produced each day to minimize the cost? - What would it cost, c(x) to produce that many fixtures?

    Linear algebra: orthanormal basis

    (See attached file for full problem description) --- For the A-matrix: 5x1 + 9x2 + 2x3 = 24 9x1 + 4x2 + x3 = 25 2x1 + x2 + x3 = 11 construct an orthonormal basis with a1 and then a2 and then a3. Next, expand the given vector b in terms of those vectors. ---

    Solve by drawing

    SOLVE BY DRAWING THE APPROPRIATE GRAPH AND SHOW WORKING OUT X3-X2-5X+2=0

    Field Extension/Transcendental

    Let F be an extension field of K. If u is an element of F is transcendental over K, then show that every element of K(u) that is not in K in also transcendental over K. Hint for proof: Suppose y is an element of K(u). Then for some g(x), h(x) elements of K[x], we have y = g(u)/h(u). Assume that y is algebraic over K and think

    Find the values of x for any points where the curve

    Find the values of x for any points where the curve 2x^2+xy+3y^2=54 has a vertical tangent. Choices are:A. (18*(square root of 46))/23, B. (18*(square root of 20))/5, C. (5*(square root of 3))/23, D. (16*(SQAURE ROOT OF 23))/25 OR NONE OF THESE. Please show work.

    Several Problems

    (See attached file for full problem description) --- 2. Page 237, problem 102 Increasing deposits. At the beginning of each year for 5 years, an investor invests in a mutual fund with an average annual return of r. The first year she invest $10; the second year, she invest $20; the third year; she invests $30; the fo

    Eisenstein's Criterion

    (See attached file for full problem description with proper equations) --- Let p be an odd prime and let be the p-th cyclotomic polynomial. Use the fact that to show that , and so find coefficients such that . Hence show that is irreducible over by using Eisenstein's criterion.

    Cost per square inch

    Calculate the cost per square inch of pizza of the following: 14" square pizza for $10.99 18" round pizza for $10.99 two 12" round pizzas for $10.99

    Some algebra and log questions.

    (See attached file for full problem description with proper equations) --- ? Can you please show me how to solve the following problems without a calculator? thanks ? x^(2/3)=9 ? (2/3)^-x= (27/8) ? 27^(4/3)=x ? 2.8=-2.5 ln (x-70/98.6-70) ? 2/3 [(log2(x-2)+log2(x+2)-log2(x-3)] ===

    Pollard-Rho

    Use the Pollard-Rho method... (See attached file for full problem description)

    Logarithms Equation

    A) Solve the equation for x logx + log 4x=16 b) Rearrange to make x the subject y = 2logx.

    Distance Between Ships

    At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 19 knots. How fast is the distance between the ships changing at 4 PM, in knots? (1 knot is a speed of 1 nautical mile per hour) - The final result is not around 25 (i.e. 25.XX is not correct). Please check