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Suppose that η : R^n→ R^n is a Lipschitz function with Lipschitz constant αband 0≤α<1. Prove that the function F :R^n →R^n given by F (x) = x + η(x) is bijective. Hint: Use a contraction argument
Find the area of the "triangular" region in the first quadrant bounded on the left by the y-axis and on the right by the curves y
shipments of light bulbs are acceptable to a distributor if the mean life is at least 1000 hours. a random sample of 48
an airplane flies 490miles with the wind and 330 against the wind in the same length of time. if the speed of the wind is 20, what is the speed of the airplane in still air?
Let f be a function f . Z → Z x Z such that f(n) = (2n, n + 3). Verify whether this function is 1-1 and whether it is onto and let f be a function f . R3 → R such that f(x, y, z) = xyz. Verify whether this function is 1-1 and whether it is onto.
people were polled on how many books they read the previous year. how many subjects are needed to estimate the number
A ball is dropped from a cliff that is 352 feet high. The distance S (in feet) that it falls in t seconds is given by the formula How many seconds (to tenths) will it take for the ball to hit the ground?
a cashier has a total of 123 bills made up of fives and tens. The total value of the money is $725. how many ten-dollar bills does the cashier have?
A triangle drawn on a map has sides of lengths 7 cm, 11 cm, and 14 cm. The shortest of the corresponding real-life distances is 92 km. Find the longest of the real-life distances to the nearest tenth of a kilometer.
What are the most signification concepts that you have learned about the physical and social domains on the basis of your reading and experience with children?
explain how the applications of integer programming differ from those of linear programming. give specific instances in
The perimeter of a swimming pool is 97m. The width is 2m more than helf of lenght of the pool, find the lenght and the width of the pool?
Let x represent the number of $20 price increases. Write expressions for the new price, the number of rented apartments, and the total revenue.
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