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Question: Let R be a polynomial ring over an infinite field k and I a graded ideal of height r. If I is minimally generated by forms of degree p ≥ 1, prove that there are forms f1,...,fm of degree p in I such that f1,...,fr is a regular sequence and I is minimally generated by f1,...,fm.
Clear glass costs $3 per square foot and stained glass costs $10 per square foot. Express the cost of the window as a function of the radius of the stained glass pane.
If local mortgage rates are 7.5%/year compounded monthly for a conventional 30-yr mortgage, what is the price range of houses they should consider?
Inverse Laplace transforms Find the inverse laplace transforms Express the following in partial fraction form Find the inverse laplace tranform
Calculate the mean and standard deviation of the random variable X associated with these data.
Find an equation for the sphere centered at (2, -4, -1) that is tangent to the y-z coordinate plane.
The meatball is being stored in the fridge at 35 degrees F. The meatball will go into a convection oven at 350 degrees F (surface is maintained at precisely 350 for the duration of cooking)
Why are small Indian retailers complaining about Amazon India, FlipKart, and Snapdeal.com which function as online bazars (vs. retailers that sell direct to end consumers) in India?
Estimate the true proportion of all Americans who are in favor of gun control legislation using a 95% confidence interval. INTERPRET the answer.
Find the median number of newspapers sold.
A herd of American buffalo (bison) can be modeled by a stage matrix similar to that for the spotted owls. The females can be divided into calves.
Consumer Credit The total amount of consumer credit has been increasing steadily in recent years. The following table gives the total U.S. outstanding consumer.
Find the limit. Use I'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. limx→∞ (1 + a/x)bx.
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