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Please help with the following problems involving group theory proofs. Provide step by step calculations along with explanations.
a) Prove that if G is a finite group and a is an element of G then for some positive m , a^m is equal to the identity of G. (Use the Pigeon hole principle)
b) Prove that if G is a finite group, H subset of G that is closed with respect to the operation of G, Then every element of H has its inverse in H.
write an equation of a line that is parallel to the y-axis and passes through the point
Problem on profit and loss.
what is the length of the longest side of a triangle that has the vertices 2 6 -4 6 and -4
The sum of two numbers is 54, and their difference is nine more than the smaller number. Find the numbers.
Find the slope of the line containing the given points: (2, -8); (-7, 3). Determine whether there is a maximum or minimum value for the given function, and find that value. f(x) = x2 - 20x +104
Car license plates in California take the form of 1RTY345. If zero cannot be used in the first position and repeats are allowed in the other 6 positions, how many license plates are possible?
On 3 consecutive passes a football team gains 7 yards, loses18yards, and gains 46 yards. What number represents the total net yardage?
if it is known that determinant of A, det(A) = alpha*delta - beta*gamma > 0, and that the trace of A, Tr(A) = alpha + delta
Given the linear equation y= -3/7x-1, find the y-coordinates of the points (-7, ), (0, ), and (7, ). Please show all of your work. Plot those points and graph the linear equation.
Find the slope of the line through the points (0, 4) and (5, 0)
Select a quadratic equation and solve it using the completing the square method. Show your work in full details.
These are two examples, one specific, and one more general, where you are given y as a function of x, and we want to find what x is in terms of y, so we want to make x the subject of the equation.
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