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Let $ {Xn}$ be a sequence of compact length spaces, $GHlim X_n=X$ (Gromov-Hausdorff convergence), and let $f_n$ be as in Exercise 7.5.9 (Burago and Burago and Ivanov). Prove that, for all large enough n, $f_n$ induces a surjective homomorphism of fundamental groups.
The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
Independent events based probability. A company operates a telephone order system for a catalogue of its outdoor clothing products. The catalogue orders are processed in three stages. In the first stage, the telephone operator enters the order int..
The expected gains & losses under each economic type of conditions are shown in the following table.
How do you write a system of linear equations in two variables? ??Explain this in words and by using mathematical notation in an equation.
Matthew currently has enough money to buy 45 toy cars. If the cost of each car was 10 cents less, Matthew could buy 5 more cars. How much money does Matthew have to spend on toy cars?
compute a 90% confidence interval for the mean serum cholesterol level of teenage males in this city. Assume that the sample was taken from a normal distribution. Round your confidence limits to 2 decimal places.
the speed of train a is 20 mph slower than the speed of train b. train a travels 220 miles in the same time it takes train b to travel 320 miles. find the speed of each train.
Find the point on the line y = 3x + 9 that is closest to the origin. (Give your answers correct to three decimal places.)
a ship travels 54km on a bearing of 13 and then travelson bearing of 156km. what is the distance of the end of the trip form the starting point ?
The upper left-hand corner of a piece of paper 8 in. wide by 12 in. long is folded over to the righthand edge as in the figure. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y?
Let R be a set with 2 laws of composition satisfying all ring axioms except the comutative law for addition
Compute the coecients of the polynomials using the term recurrence relation.
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