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When an element and its inverse are combined under and operation the result is the identity element. The identity element for multiplication is 1.
Let i be an integer with 1 <= i <= n. Let Gi* be the subset of G1 X ... X Gn consisting of those elements whose ith coorinate is any element of Gi.
Each one need only be 1 to just a few sentences - please list separately and under each fact provide any links to websites or pictures etc.
Find all the integers such that when the final digit is deleted the new integer divides the original one.
A = U X U, where U = {1, 2, 3, 4, 6, 12}, and %:A -> Q is defined by %(n, m) = n/m, where Q is the set of all rational numbers.
Let G = GL(2,R) be the general linear group. Let H=GL(2,Q) and K= SL(2,R) = {A is an element of G: det (A) =1} Show that H,K are subgroups of G.
When the number is divided by 9 the remainder is 7 and when it is divided by 5, the remainder is 1. What is A-B=?
How much money has Lose-a-digit budgeted for the year? "The amount of the budget just happens to be the smallest number of cents (other than one cent).
Let I be an open interval containing the point x.(x not), and suppose that the function f:I->R has a continuous third derivative with f'''(x)>0 for all x in I.
Given ( INTEGRAL ln square(x)dx, as x from n to n+1 ) = ( INTEGRAL ln square (n+x)dx, as x from 0 to 1 ) = ( INTEGRAL [[ln(n+x) - ln(x) + ln(n)]square]
Let f(x) and g(x) be nonzero polynomials in R[x] and assume that the leading coefficient of one of them is a unit.
Write a polynomial that represents the total cost of Materilas and Labor for producing x transmissions.
A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.
When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative.
Determining a solution (an ordered pair) from a system of equations.
Linear Algebra - Vector Spaces.Let P be the set of all polynomials. Show that P, with the usual addition and scalar multiplication of functions
Determine whether the given sets form subspaces of R2. What does the T stand for in these equations?
Prove that there are no integers x, y, and z such that x2 + y2 + z2 = 999. Provide complete and step by step solution.
16 is a non-trivial square root of 1 modulo 51; hence 51 is composite, 7 is a non-trivial square root of 1 modulo 47; hence 47 is composite
We may assume that r and s have no prime factors in common, since any common prime factors may be cancelled.
Step by step solution to this problem, starting off with how does one determine the values of x and y.
If a deck is rectangular and has an area of X2 + 6x + 8 (the 2 is squared) square feet and a width of x + 2 feet. Determine the lengths of the deck.
Express x1, x2, and L(x) in terms of polar coordinates. Describe geometrically the effect of the linear transformation.
Let f be a nonnegative integrable function. Show that the function F defined by F(x) = -8?x f is continuous by using Monotone Convergence Theorem.
Difference between mapping R3 to R2 and the reverse. What's the difference between mapping from R3 into R2 and mapping from R2 into R3?