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This assignment is a mathematical paper rather than a homework assignment. In particular do no state a problem and jump right into a solution. Segue naturally into the problems. This is quite terse, so more words and explanations are needed and it should flow like a report or paper. Some background on theorems and properties used should be provided for the reader and flow into it the assigned problems one at a time with something like "Consider the Cayley graph of...Let's determine if this has a Hamilton circuit".
When you provide background and theorems, use your own numbering. Do not say, for example "Theorem 14.4". Assume the reader does not own the textbook.
Show that the Cayley digraph given in Example 7 has a Hamiltonian path from e to a.
Example 7: Q4 = {a,b |a4 = e, a2 = b2, b-1ab = a3}
Prove that the Cayley digraph given in Example 6 does not have a Hamiltonian circuit. Does it have a Hamiltonian path?
Example 6: A4 = {(12)(34),(123}
One of the advantages of rational functions is that even rational functions with low-order polynomials can provide excellent fits to complex experimental data.
Find the range of f(x)=2x+4 for the domain {-4,-1,3,4].
the population of a city was 94 thousand in 1992. the exponential growth rate was 1.6 per year. find the exponential
solve the characteristic equation above for the roots m1 and m2. hint you may need to solve by factoring or by using
what is the smallest cube integer of the form n to the third that is divisible by 16 but is not a square number b to
The length of a rectangular swimming pool is 2x - 1 meters, and the width is x + 2 meters. Write a polynomial A(x) that represents the area. Find A(5).
find the sum upto n terms of the following sequence 3+33+333+... n terms
Automobiles usually depreciate in value over time. Often a newer automobile may be worth only 80% of its previous year's value. Suppose that a car is worth $25,000 new.
Describe two laws of exponents and provide an example illustrating each law. Explain how to simplify the expression. How do the laws work with rational exponents?
Gram-Schmidt Orthogonalization - Maple plot - , Calculate ?P and ?N by the formulas given above. Use Step I of the Maple supplement to plot your results and to check your calculations.
solve the following system of inequalities by graphing.5x - 4y ge -203x - 2y le -8y ge
Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x = 5.
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