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Let D be a squarefree integer, and let 0 be the ring of integers in the quadratic field Q(√D). For any positive integer f prove that the set Of = Z[fw] = {a + bfw | a, b E Z} is a subring of 0 containing the identity. Prove that [O:Of]= f (index as additive abelian groups). Prove conversely that a subring of 0 containing the identity and having finite index f in 0 (as additive abelian group) is equal to Of. (The ring Of is called the order of conductor f in the field Q(√D). The ring of integers 0 is called the maximal order in Q(√D).
Elimination method for solving the system of equations.
One measure used to describe a data set is the range. The range of a data set is given by the difference between the max and the min of the set. Find the range of each set of numbers. 7, 7, 5, 4, 1, 9, 8, 8, 8, 5, 2.
Simplify. Use absolute-value notation when necessary.12 (cubed)v-----------(square root symbol)(-10) 12 (twelfth power)
Compute the value of y in the mod 9 system.
Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.
How do we write the equation of a horizontal line? What would be an example?
Use elimination or substitution method equations.
Make a graph for the equation
If all of the tickets are sold, receipts from the $5.00 tickets will be $50.00 less than those from the $2.00 tickets. How many $5.00 tickets were printed?
If I have a quadratic equation (y = x^2 - 2x - 8)) that graphs to a parabola with a minimum value at the vertex (1, -9), how would you find the maximum value for the equation?
Explain, using a diagram, how the following problems illustrate the two interpretations of division: partitive division ans measurement division.
Solving maximization problem
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