Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Textbook Question
Chapter P, Problem 56PS
What is the maximum number of points of intersection of n distinct lines?
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Problem 11 (a) A tank is discharging water through an orifice at a depth of T
meter below the surface of the water whose area is A m². The
following are the values of a for the corresponding values of A:
A 1.257 1.390
x 1.50 1.65
1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650
1.80 1.95 2.10 2.25 2.40 2.55 2.70
2.85
Using the formula
-3.0
(0.018)T =
dx.
calculate T, the time in seconds for the level of the water to drop
from 3.0 m to 1.5 m above the orifice.
(b) The velocity of a train which starts from rest is given by the fol-
lowing table, the time being reckoned in minutes from the start
and the speed in km/hour:
| † (minutes) |2|4 6 8 10 12
14 16 18 20
v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0
Estimate approximately the total distance ran in 20 minutes.
-
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p − 1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
p-1
2
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
23
32
how come?
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
The set T is the subset of these residues exceeding
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
Let n = 7, let p = 23 and let S be the set of least positive residues mod p of the first (p-1)/2
multiple of n, i.e.
n mod p, 2n mod p, ...,
2
p-1
-n mod p.
Let T be the subset of S consisting of those residues which exceed p/2.
Find the set T, and hence compute the Legendre symbol (7|23).
The first 11 multiples of 7 reduced mod 23 are
7, 14, 21, 5, 12, 19, 3, 10, 17, 1, 8.
23
The set T is the subset of these residues exceeding
2°
So T = {12, 14, 17, 19, 21}.
By Gauss' lemma (Apostol Theorem 9.6),
(7|23) = (−1)|T| = (−1)5 = −1.
how come?
Chapter P Solutions
Nature of Mathematics (MindTap Course List)
Ch. P - IN YOUR OWN WORDS The prologue provides a...Ch. P - IN YOUR OWN WORDS The epilogue for this text...Ch. P - HISTORICAL QUEST What are the five chronological...Ch. P - HISTORICAL QUEST Select what you believe to be the...Ch. P - HISTORICAL QUEST Select what you believe to be the...Ch. P - HISTORICAL QUEST Select what you believe to be the...Ch. P - HISTORICAL QUEST Select what you believe to be the...Ch. P - HISTORICAL QUEST Select what you believe to be the...Ch. P - IN YOUR OWN WORDS This prologue has 60 problems as...Ch. P - IN YOUR OWN WORDS Problems 11-60 are included to...
Ch. P - In mathematics, is is important to read the...Ch. P - In mathematics, is is important to read the...Ch. P - How many people must be in a room to be sure that...Ch. P - In mathematics, is is important to read the...Ch. P - If a year had two consecutive months with a Friday...Ch. P - On Saturday evenings, a favourite pastime of the...Ch. P - In mathematics, is is important to read the...Ch. P - In mathematics, is is important to read the...Ch. P - If the population of the world on October 12,2002,...Ch. P - Prob. 20PSCh. P - In mathematics, is is important to read the...Ch. P - Prob. 22PSCh. P - In mathematics, is is important to read the...Ch. P - In mathematics, is is important to read the...Ch. P - In mathematics, is is important to read the...Ch. P - In mathematics, is is important to read the...Ch. P - In mathematics, is is important to read the...Ch. P - If a group of 50 persons consists of 20 males, 12...Ch. P - In mathematics, is is important to read the...Ch. P - Prob. 30PSCh. P - What is the 1,000th positive integer that is not...Ch. P - In mathematics, is is important to read the...Ch. P - How many trees must be cut to make a trillion...Ch. P - Prob. 34PSCh. P - Critique the statement given in the news clip.Ch. P - In mathematics, is is important to read the...Ch. P - Prob. 37PSCh. P - The map shows the percent of children ages 19-35...Ch. P - Prob. 39PSCh. P - Find limn(1+1n)n.Ch. P - Prob. 41PSCh. P - Prob. 42PSCh. P - Suppose the percentage of alcohol in the blood t...Ch. P - Prob. 44PSCh. P - A map of small village is shown in Figure 8. To...Ch. P - A hospital wishes to provide for its patients a...Ch. P - Prob. 47PSCh. P - Find the smallest number of operations needed to...Ch. P - If log2x+log4x=logbx, what is b?Ch. P - Supply the missing number in the following...Ch. P - Prob. 51PSCh. P - Answer the question asked in the news clip from...Ch. P - Five cards are drawn at random from a pack of...Ch. P - What is the sum of the counting numbers from 1 to...Ch. P - The Kabbalah is a body of mystical teaching from...Ch. P - What is the maximum number of points of...Ch. P - The equation P=153,000e0.05t represents the...Ch. P - The Egyptians had an interesting, pictorial...Ch. P - If you start with 1 and double the amount received...Ch. P - Consider two experiments and events defined as...
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