Explore BrainMass

Explore BrainMass

    Algebra

    BrainMass Solutions Available for Instant Download

    Expressing Roots of Quadratic Equations

    If (x + 2)(x - 4) = 0 indicates that x + 2 = 0 or x - 4 = 0, explain why (x + 2)(x - 4) = 6 does not mean x + 2 = 6 or x - 4 = 6. Could we solve the equation using x + 2 = 3 and x - 4 = 2 because (3)(2) = 6?

    Remainders of Euclidean Algorithms

    Let b = r_0, r_1, r_2, ... be the successive remainders in the Euclidean Algorithm applied to a and b. Show that every 2 steps reduces the remainder by at least one half. In other words, verify that r_{i+2} < (1/2)r_{i}, for every i = 0,1,2,.... Conclude that the Euclidean algorithm terminates in at most 2log_{2}(b) steps, where

    Divisibility of Sequences

    Let m, n be in N, with m, n >= 1 and n odd. Let S_m = 1^n + 2^n + 3^n + ... + m^n. Prove that S_m is divisible by 1+2+...+m.

    Solving Equations Solutions

    Where the solution is x = 104/25 please break this problem down to solution showing each stage of problem solving.

    Factoring

    What is factoring by grouping? When factoring a trinomial, why is it necessary to write the trinomials in four terms?

    Solving Equations Functions.

    I) f(x) = 2 - (square root x) for x>= 0 Given that |f(x)| = k has two distinct roots, determine the possible values of the constant k. ii) Solve for 0 < x < 90, the equation 3sin6xcosec2x = 4

    Writing and Solving Equations from Word Problems

    Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed, he discovered that one side was actually 2 feet longer than he thought and the other was actually 2 feet shorter than he thought. How much less area does he have than he thought he had?

    Generating a Commutative Ring

    Let a commutative ring R be generated by {a_1, a_2, ..., a_n} such that [a_1, a_2, ... , a_n] = {(a_1xr_1) + (a_2xr_2) + ... + (a_nxr_n) for r_1, ..., r_n in set of Reals}. I need to show this set is an ideal. Do I just need to show that it satisfies the commutative properties of the ideal?

    The Maximum Height on a Building the Ladder Can Reach

    A 30 feet ladder is used by fire fighters is a safe only when it leans against a building at an angle of 60 degrees or less to the ground. What is the maximum height on a building the ladder can reach? Round to the nearest hundredth.

    Diagonal Square Path Through a Park

    The village green is the shape of a square. Along the diagonal of the square is a path through the park. The path is 80 feet long. Find the area of the park. Round to the nearest tenth, if necessary.

    Recurrence relation

    1. If a person invests in a tax-sheltered annuity, the money invested, as well as the interest earned, is not subject to taxation until withdrawn from the account. Assume that a person invests $2000 each year in a tax-sheltered annuity at 10 percent interest compounded annually. Let An represent the amount at the end of n year

    Fibonacci Sequences Solved

    Let (f_k) be the Fibonacci sequence, show that: a) For every integer n>= 0, we have f_4(n+1) = 3f_4n+1 + 2f_4n b) Use a) in order to prove by induction that ∀n є N, 3 | f_4n

    Writing Equations from Word Problems : Speed and Distance

    A pilot flies from Toledo to Chicago, which lies 280 mi directly west. Her plane can fly at 120 mi/hr. She ignores the wind and heads directly west. However, there is a 25 mi/hr wind blowing from the south. a) Write the equation that describes the effect of the wind b) Write the equation that describes the plane's contr

    Factor Groups of Non-Abelian Groups

    Let G be a nonabelian group and Z(G) be its center. Show that the factor group G/Z(G) is not a cyclic group. We know if G is abelian, Z(G)=G. But now if it is not abelian, can we simply say because G is not cyclic, then any factor group will not be cyclic either? or is there more to it?

    Solving an Initial value problem by using Taylor's method

    Use Taylor's method with h = 0.05 to approximate the solution, and compare it with, actual values of y. See attached file for full problem description. (5.3) 6. Given the initial-value problem , , with exact solution : a. Use Taylor's method with h = 0.05 to approximate the solution, and compare it with, actual va

    R-modules, Ideals and Submodules

    Let R=Z[X] and let M=(2,X) be the ideal generated by 2 and X considered as a submodule of R. Show that {2,X} is not a basis of M.

    Finding the Sum of a Convergent Series

    Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges find its limit. Please see the attached file for the fully formatted problems.

    Contour Integrals

    Calculate the integral using contour integration. Complete explanation is required. integral(0-> &#8734;)logxdx/(1+x^2)^2 keywords: integration, integrates, integrals, integrating, double, triple, multiple

    Intersection of planes and lines

    Find all points of intersection of the following planes, and describe what shape the intersection makes in 3 space 2z -10 =0 x +y +z -5 =0 -3x -3y =0

    Lines and Planes Minimums

    Show that the following two planes are parallel and find the minimum distance between them: x-2y+5z+4=0 -2x +4y -10z +9 =0