
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
14th Edition
ISBN: 9780134677972
Author: Barnett
Publisher: PEARSON
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Textbook Question
Chapter DPT, Problem 40E
In Problems 37-40, solve for
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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 DPT Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Ch. DPT - Replace each question mark with an appropriate...Ch. DPT - Problems 2-6 refer to the following polynomials:...Ch. DPT - Problems 2-6 refer to the following polynomials:...Ch. DPT - Problems 2-6 refer to the following polynomials:...Ch. DPT - Problems 2-6 refer to the following polynomials:...Ch. DPT - Problems 2-6 refer to the following polynomials:...Ch. DPT - In Problems 7 and 8, perform the indicated...Ch. DPT - In Problems 7 and 8, perform the indicated...Ch. DPT - In Problems 9 and 10, factor completely. x2+7x+10Ch. DPT - In Problems 9 and 10, factor completely. x32x215x
Ch. DPT - Write 0.35 as a fraction reduced to lowest terms.Ch. DPT - Write 78 in decimal form.Ch. DPT - Write in scientific notation:...Ch. DPT - Write in standard decimal form: A2.55108B4.06104Ch. DPT - Indicate true (T) or false (F): (A) A natural...Ch. DPT - Give an example of an integer that is not a...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - Each statement illustrates the use of one of the...Ch. DPT - Prob. 32ECh. DPT - Multiplying a number x by 4 gives the same result...Ch. DPT - Find the slope of the line that contains the...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - In Problems 37-40, solve for x. x2=5xCh. DPT - In Problems 37-40, solve for x. 3x221=0Ch. DPT - In Problems 37-40, solve for x. x2x20=0Ch. DPT - In Problems 37-40, solve for x. 6x2+7x1=0
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