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Question: Let A be an affine algebra over a field k and let k ⊂ K be a field extension. Prove
(a) dim(A) = dim(A ⊗k K).
(b) depth(A) = depth(A ⊗k K) if A is a standard algebra.
A boat race runs along a triangular course marked by buoys A, B, and C. The race starts with the boats headed west for 3600 meters. The other two sides of the course lie to the north of the first side, and their lengths are 1500 meters and 2800 me..
Graph the system of inequalities. Show (by shading in) the feasible region.
Its center of mass is located at a distance of s=0.120 m from the center of the circle. If the disk is allowed to oscillate side to side as a pendulum, what is the period of oscillations?
Find the Fourier series for the odd extention of the function f(x)=5, 0
Calculate also a 90% interval estimate for the average of all customers' actual account balances in which a computer-generated account balance is the same as that of Mr. Jones (part c). Interpret your results.
Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.
Factor the trinomial and enter your answer below. Write each factor as a polynomial in descending order.
What proportion of the company's callers are put on hold for at least 4.8 minutes? Should the company hire more operators?
The current i in the circuit is the instantaneous time rate of change of the charge. Find the expression for i as a function of t.
The time it takes you to get to campus varies inversely as your driving rate. Averaging 20 miles per hour in terrible traffic, it takes you 1.5 hrs to get to campus. How long would the trip take averaging 60 miles per hour?
A boat is headed across a river with a velocity relative to water) that can be represented as (6.5 + 1.7) mi/h. The velocity of the river current can be represented as (- 1.1 - 4.3j) mi/h. Express the resultant velocity of the boat in polar from.
on august 31 2010 a company purchased 10000 shares of stock for 30 per share. management recorded the stock in the
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