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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.
Create a rule such that f(x1,y2)=x2 and f(x2,y3) = x3. The rule must be such that after the sequence has been created, if you are given x3,y3,x2 and y1, then x1 and y2 can be determined i.e y2 = g(x2,x3)
Sketch by hand the graph y=[[x]] by first tabulating the values pf [[1]] for several numbers x. Then compare your graph with the plot from a graphing calculator.
The population of a city is 50,000 in 2008 and is growing at a continuous yearly rate of 4.5%. Give the population of the city as a function of the number of years since 2008. Sketch a graph of the population against time.
Use an excel spreadsheet with the data provided. Prepare a graph of activity vs. seconds. Use a trend line to produce the best exponential line through the points.
Show manual work (by hand) step by step to reach the optimal answer (i.e., don't just provide a final answer and don't use a computer program to find a solution). Provide also a summary of your solution.
Please see the following example. Do not use any version of this example in your own post. You may use other variables besides x and y, such as x and W depicted in the following example. Be sure to reference all sources using APA style.
If there is a problem with a large number of equations and variables then the elimination method would be preferable to the substitution method. After all, it would break down the problem and/or equations in an easier manner.
Write a polynomial of least degree with real coefficients
What kind of slope you would get if your employer decided to pay you the same salary whether you work overtime or not? Define the dependent and independent variables in this situation.
Using the straight-line method, depreciation expense for 2007 and the equipment book value at December 31, 2007 would be:
First-class postage (for the first ounce) was $.20 in 1981 and $.37 in 2002. Assume the cost increases according to an exponential growth function.
Suppose a culture of bacteria starts with 5000 bacteria. After one hour, the count is 6000. Find an exponential equation that models the number of bacteria in hours. Keep at least 4 decimal places in your formula for rounded values. Find the doubling..
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