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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).
Why can't the answer for these linear inequalities be simply the line y = mx + b? Why do we have to do all the shading?
What does it mean when something grows or decays exponentially? How is that different then rising or falling linearly? Give an example of a real life application of exponential growth or decay. Include the link to a website to show this.
The algebraic equation of cost functions
If there is also a zero at this point, then what happens at the pole? We know that zero divided by zero is indeterminate, but if there is a zero and a pole at the same point, what is a sensible definition of the function at this point?
Simplify the expression. Assume that variables represent non- zero real numbers.
1. The format of telephone numbers in North America is specified by a numbering plan. A telephone number consists of 10 digits, which are split into a three-digit area code, a three-digit office code, and a four-digit station code.
You have been asked to give a presentation on the relation between race and social inequality in the United States on the following issues: What is race?
hi ...... ltbrgtit is math liner algebra the question is on the attach file ltbrgt the assignment due. at
The top of a tower is a sphere with a diameter of 40ft. A layer of paint 0.08 inches thick is applied to the sphere. Approximate the volume of the paint that is used.
In exercise (1), show that W is a subspace of V. Let { } be a basis of W. Show that { } is a basis of V.
you must show your work on each of the following questions.rewrite y x2 14x 29 in general form.rewrite y 3x2 - 24x
Maximizing the profit.
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