Abstract Algebra Answers

Prove that every abelia group G is A module over the Ring of integer I.
The sub module of a unit all R - module M generation by a sub set S of M consist of all Linear combination of the element in S.

design a roller coaster using 4 quadratic equations and one linear equation. maximum height 25 m, next dip 0.5 m next peak 12.5 m and then a horizontal run out at 1.0 m off ground. For the equation y=a(x - b)^2 + c, the radius of curve to be = 1/2a and all slope steepness are the same = 2a(x-b).what will the 5 equations be to design the roller coaster.

How many onto functions are there from an n-element set to an m-element set?

How many self dual functions are possible with four boolean variables?

place 10 dishes along the 4 edges of a table so that each edge has the same amount of dishes

Let V={1,2,3,4} and let f={(1,3),(2,1),(3,4),(4,3)} and g={(1,2),(2,3),(3,1),(4,1)}. Find f o g.

hey, I'm stuck with parabolas. we're asked to graph them and find vertex and zeros.. please help

let a be a fixed element of a group G. show that H={ax=xa , where x is the element of G} is a subgroup of G.

Please show that the vector a is orthogonal to the hyperplane H = H(a,€); that is, if u and v are in H, then a is orthogonal to u - v.

list all the proper subgroup of the multiplicative Z18

Let G be a group with respect to binary operation and a be an arbitrary element of G. Show that H={x:x E G, x binary operation a=a binary operation x} is a subgroup G.

Show that the set {x:x E I, 5/x} is a subgroup of the additive group I.