Path To College Mathematics
1st Edition
ISBN: 9780134654409
Author: Martin-Gay, K. Elayn, 1955-
Publisher: Pearson,
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Chapter E, Problem 28ES
Solve. See Examples 2, 5, and 6.
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Students have asked these similar questions
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 E Solutions
Path To College Mathematics
Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write a direct variation equation, y=kx, that...Ch. E - Write an inverse variation equation, y=kx, that...Ch. E - Write an inverse variation equation, y=kx, that...
Ch. E - Write an inverse variation equation, y=kx, that...Ch. E - Write an inverse variation equation, y=kx, that...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use k...Ch. E - Write en equation to describe each variation Use...Ch. E - Solve. See Examples 2, 5, and 6. y varies directly...Ch. E - Solve. See Examples 2, 5, and 6. y varies directly...Ch. E - Solve. See Examples 2, 5, and 6. y varies directly...Ch. E - Solve. See Examples 2, 5, and 6. y varies directly...Ch. E - Solve. See Examples 2, 5, and 6. z varies directly...Ch. E - Solve. See Examples 2, 5, and 6. s varies directly...Ch. E - Solve. See Examples 2, 5, and 6. a varies...Ch. E - Solve. See Examples 2, 5, and 6. p varies...Ch. E - Solve. If needed, round money amounts to 2 decimal...Ch. E - Solve. If needed, round money amounts to 2 decimal...Ch. E - Solve. If needed, round money amounts to 2 decimal...Ch. E - Solve. If needed, round money amounts to 2 decimal...Ch. E - The distance a spring stretches varies directly...Ch. E - The weight of an object varies inversely as the...Ch. E - For a constant distance, the rate of travel varies...Ch. E - The distanced that an object fails is directly...Ch. E - The distance needed for a car to stop d, is...
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