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1. Let A ⊆ R be a set, let f, g: A ?R be functions and let k ∈ R. Suppose that f and g are uniformly continuous. Prove that f + g are uniformly continuous.
2. Let [a, b] ⊆R be a closed bounded interval, and let f : [a, b] ?[a, b] be a function. Suppose that f is continuous. Prove that there is some c ∈ [a, b] such that f(c) = c. The number c is call a fixed point of f.
In triangle ABC, angle C is a right angle. Find the measure of angle B if side b = 19 m and side c = 89 m. Round to the nearest degree.
Suppose you are a hospital dietitian and you have prepared ten luncheon menus for next week. How many orderings of seven menus taken from the ten menus are possible?
An apartment building has seven elevators. Each elevator stops on at most six floors. You can get to any one flooor from any other floor without changing elevators (if you take the right elevator). What is the largest number of floors that buildin..
Jerry has a total of 23 marbles. The marbles are either blue or green. He has three more blue marbles than green marbles. How many green marbles does he have?
At a sand and gravel plant, sand is falling off a conveyor belt and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude
Suppose that n = pqr is the product of three distinct primes. How would an RSAtype of cryptosystem work in this case? In particular, what relation would e and d satisfy?
Each student at State University has a student I.D. number with a specific pattern: The ID begins with one of these letters: {A, B, C, D, E}, which is followed by a four-digit number,
The J.P. Atkins Company will soon be introducing a new product. Estimates have been made of the monthly profit that would be generated by this product for each of four alternative values of the monthly production rate, as shown below.
A fence is being built to enclose a backyard. The yard is 150 ft wide by 325 ft long. The back of the house will act as on side of the fence. Fencing sells for 13.00 dollars per ft. How much will the fencing cost?
Julia Robertson is a senior at Tech, and she's investigating differ- ent ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia k..
the intensity of light from a light bulb, measure in watts (w), varies inversely as the square of the distance (d) from the light bulb. Suppose I is45 w/m(squared) when the distance is 6m.
find the lengths of both circular arcs of the unit circle connecting the point 10 and the endpoint of the radius that
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