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Let R be a PID. Consider the Diophantine equation ax+by=N where a,b and N are integers and a,b are nonzero. Suppose x_0, y_0 is a solution: ax_0+by_0=N. Prove that the full set of solutions to this equation is given by
x = x_0 + (mb/gcd(a,b))
y = y_0 - (ma/gcd(a,b))
as m ranges over the integers.
Vital information about Quantitative analysis:Networks, PERT, critical path. A project was planned using PERT with three times estimates. The expected completion time of the project was determined to br 40 weeks
Investments. William opened two investment accounts for his grandson's college fund. The first year, these investments, which totaled $18,000, yielded $831 in simple interest. Part of the money was invested at 5.5% and the rest at 4%. How much was..
Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section? Please show work.
What is the probability of getting the indicated result
Find the p-value associated with the test of hypothesis
A person is given 4 coins each with equal and independent probabilities of being a nickel , a penny, a dime or a quarter. What is the probability the person has been 37 cents
In Algebra, when using the addition method, how can you tell if a system of linear equations has infinitely many solutions?
Until recently, with the advent of cellular phones, modems, and pagers, the area codes in the United States and Canada followed a certain system
Find the expected value (to you) of the game. If you play one game would you expect to win or lose the game? Explain.
Let K be a normal subgroup of G, and both K and G/K are simple. Show that either K is the only nontrivial proper subgroup of G, OR G is isomorphic to K x (G/K).
Trigonometric identities to find length of the guy wire.
Construct an explicit deformation retraction of the torus with one point deleted onto a graph consisting of two circles intersecting in a point, namely, longitude and meridian circles of the torus.
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