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One property of rational numbers is that they are dense, that is, between any two rational numbers is another rational number. Given two arbitrary rational numbers, show how you could find another rational number between them.
A heavy rope, 30 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 70 ft high. How much work W is done in pulling half the rope to the top of the building?
Find the Maclaurin polynomial Tn.x/ (for a general n) for the function f .x/ D 2x.
How much time should the fisherman allow for the painting of the hull, if the hull were composed of two sides, each 28.5 feet by 10.50 feet?
a steep mountain is inclined 79 degrees to the horizontal and rises 3100 ft. above the surrounding plain. a cable car is to be installed from a point 900ft from the base of the mountain. find the shortest length of cable needed?
Suppose that a "skew" product of vectors in R2 is defined by (u,v)=u1v1-u2v2. Prove that (u,v)squared >equal too (u,u)(v,v). (NOTE; This is just the reverse of the Cauchy- Schwartz inequality for the ordinary dot product.)
Give a real-life example of a situation in which you would use a system of inequalities, and for which the solution must be in the first quadrant.
Explain how you would use probability, statistics and geometry in the computer forensics field, give one example of each to illustrate the concept.
the vertices of the trapezoid ar ethe origin along with A (4m, 4n), B (4q, 4n), and C (4p, 0). Find the midpoint of the midsegment of the trapezoid.
The cost of renting tuxes for the Choral Society's formal is $20 down, plus $88 per tux.
Probability - poker fullhouse. A game of poker is played with an ordinary deck of 52 cards, and each player is dealt a hand of 5 cards chosen at random
A school had a very unusual tradition involving its 1000 students and its 1000 lockers. On opening day, after the head of the school had closed all the lockers, a student walked by and opened every single one.
Prove the Second Isomorphism Theorem: If A is an ideal of R and S is a subring of R, then S+A is a subring, A, and (S intersecting A) are ideals of S+A and S, respectively, and (S+A)/A isomorphic to A/(S intersecting A).
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