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Let R be an integral domain, "m" a maximal ideal. Let S=R-m
a)Prove that S^-1R is a local ring.
b)Suppose R=Z, m=(5). Describe S^-1R.
Select five values for x to plug into the linear function, P(x)=10x-7 and prepare a table of values
Today you visited the R&D (Research and development) development of a pharmaceutical manufacturer. The people in this lab have to calculate the recommended dosage of the products they are developing. Medicine is expressed as a function of the conc..
Prove or disprove the following statements. (a) If a; b 2 Z, a; b > 0, and a2 j b3, then a j b.(b) If a; b 2 Z, a; b > 0, and a2 j b2, then a j b.
Show that a polynomial function is continuous at every point of R. Show that a rational function (a quotient of two polynomial functions) at every point where it is defined.
Two cars leave a restaurant at the same time and travel in opposite directions. One averages 50 miles per hour and the other averages 40 miles per hour. After how long will they be 216 miles apart?
In each case, determine whether or not the given set is linearly independent and compute the dimension of the linear subspace spanned by the set.
Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation
Solve the problem graphically. Be sure to check your solution. 4y = x + 4x = y + 2
Simplify for the unknown variable
find out which of the four techniques (the Method of Addition, the Method of Substitution, Gauss-Jordan Elimination, and Cramer's Rule) is used in the majority of these types of software packages. Give your opinion why this technique is the one mo..
compare and contrast permutations and distinguishable permutations. provide a formula for each. state the fundamental
how do you use all four basic mathematical operations addition subtraction multiplication and division in combination
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