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a 25 foot rope is used to keep a boat 18 feet away from a dock. The rope connects to the boat at the level of the water. What is the angle formed between the rope and the level of the water to the nearest tenth of a degree?
How many mare gallons of water will it take to fill the tank?
A computer programming team has 12 members. How many ways can a group of 7 (out of the 12 members) be chosen to work on a special project? Explain.
Prove that the element K=k1+k2+....km is the center of the group ring R[G]. Let K1,....Kr be the conjugacy classes of G and for each Ki let Ki be the element of R[G] that is the sum of the members of Ki.
A rectangular field has an area of exactly 1 square mile. if the field has a length of 250 yards and 3 inches, what is the width of the field? Give your answer in feet and inches, and round to the nearest inch. What is the perimeter of this field?
Evaluate the matrix of transformation
A large bag of marble contains 117 blue marbles, 229 red marbles, and 104 yellow marbles. What percent of the marbles are blue?
A window is constructed from a rectangular sheet of glass of height h with a semicircular piece of glass at each end of radius r.
Important information about Probability and Expected Value. Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that the second marble is blue, given that the firs..
if 150 grams of water at 30 degrees celsius are mixed with 200 grams of water at 100 degrees celsius, what is the final temperature of the water?
Using one of the tests for convergence (comparison, limit, integral, nth term, etc.), show whether the following series converges or diverges:
Use linear approximation, the tangent line approximation, to approximate the following: Note: the correct answer are different from the calculator computed values
Suppose that E is a normed linear space, and C is a subset. Prove that C is weakly bounded if and only if C is norm bounded. Conclude that weakly convergent sequences in E are bounded.
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