The manager of a cable company that offers both digital TV and high-speed Internet is trying to arrange his service calls efficiently. He wants to divide the people awaiting service into groups based on whether they need TV or Internet service so that his techs can concentrate on one type of service each day. If there are 40 people waiting for TV service and 32 waiting for Internet service, and he wants to schedule the same number of visits each day, what’s the greatest number of visits he can schedule each day?
The manager of a cable company that offers both digital TV and high-speed Internet is trying to arrange his service calls efficiently. He wants to divide the people awaiting service into groups based on whether they need TV or Internet service so that his techs can concentrate on one type of service each day. If there are 40 people waiting for TV service and 32 waiting for Internet service, and he wants to schedule the same number of visits each day, what’s the greatest number of visits he can schedule each day?
Solution Summary: The author explains that the greatest number of visits the manager can schedule per day is 8 visits. The common factors of 40 and 32 are 2, 2 and 2.
The manager of a cable company that offers both digital TV and high-speed Internet is trying to arrange his service calls efficiently. He wants to divide the people awaiting service into groups based on whether they need TV or Internet service so that his techs can concentrate on one type of service each day. If there are 40 people waiting for TV service and 32 waiting for Internet service, and he wants to schedule the same number of visits each day, what’s the greatest number of visits he can schedule each day?
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 5 Solutions
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