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Concept explainers
The Hubert Hotel is an imaginary hotel created by the mathematician
David Hubert (1862—1943). The hotel has an infinite number of rooms. Each room is numbered with a natural number—room 1, room 2, room 3, and so on. Search the Internet for information on Hilbert’s Hotel. Write a few paragraphs that explain some of the Interesting questions that arise when guests arrive to stay at the hotel.
Mary Pat Campbell has written a song about a hotel with an infinite number of rooms. Her song is titled Hotel Aleph Null—yeah. Here are the lyrics for the chorus of her song, which i to be sung to the tune of Hotel California by the Eagles (Source: http//www.marypat.org/mathcamp/doc200l/hellrelays.html#hotel). 4 hotel Aleph Null—yeah
Welcome to the Hotel Aleph Null—yeah
What a lovely place (what a lovely place)
Got a lot of space Packin’ em in at the Hotel Aleph Null—yeah
Any time of year You can find space here
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Chapter 2 Solutions
WebAssign Printed Access Card for Aufmann/Lockwood/Nation/Clegg's Mathematical Excursions, 4th Edition, Single-Term
- Determine whether the lines L₁ (t) = (-2,3, −1)t + (0,2,-3) and L2 p(s) = (2, −3, 1)s + (-10, 17, -8) intersect. If they do, find the point of intersection.arrow_forwardConvert the line given by the parametric equations y(t) Enter the symmetric equations in alphabetic order. (x(t) = -4+6t = 3-t (z(t) = 5-7t to symmetric equations.arrow_forwardFind the point at which the line (t) = (4, -5,-4)+t(-2, -1,5) intersects the xy plane.arrow_forward
- Find the distance from the point (-9, -3, 0) to the line ä(t) = (−4, 1, −1)t + (0, 1, −3) .arrow_forward1 Find a vector parallel to the line defined by the parametric equations (x(t) = -2t y(t) == 1- 9t z(t) = -1-t Additionally, find a point on the line.arrow_forwardFind the (perpendicular) distance from the line given by the parametric equations (x(t) = 5+9t y(t) = 7t = 2-9t z(t) to the point (-1, 1, −3).arrow_forward
- Let ä(t) = (3,-2,-5)t + (7,−1, 2) and (u) = (5,0, 3)u + (−3,−9,3). Find the acute angle (in degrees) between the lines:arrow_forwardNo chatgpt pls will upvotearrow_forwardA tank initially contains 50 gal of pure water. Brine containing 3 lb of salt per gallon enters the tank at 2 gal/min, and the (perfectly mixed) solution leaves the tank at 3 gal/min. Thus, the tank is empty after exactly 50 min. (a) Find the amount of salt in the tank after t minutes. (b) What is the maximum amount of salt ever in the tank?arrow_forward
- Draw a picture of a normal distribution with mean 70 and standard deviation 5.arrow_forwardWhat do you guess are the standard deviations of the two distributions in the previous example problem?arrow_forward1 What is the area of triangle ABC? 12 60° 60° A D B A 6√√3 square units B 18√3 square units 36√3 square units D 72√3 square unitsarrow_forward
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