Six teams ( A , B , C , D , E , and F ) are entered in a softball tournament. The top two seeded teams ( A and B ) have to play only three games; the other teams have to play four games each. The tournament pairings are A plays against C , E , and F ; B plays against C , D , and F ; C plays against every team except F ; D plays against every team except A ; E plays against every team except B ; and F plays against every team except C . Draw a graph that models the tournament.
Six teams ( A , B , C , D , E , and F ) are entered in a softball tournament. The top two seeded teams ( A and B ) have to play only three games; the other teams have to play four games each. The tournament pairings are A plays against C , E , and F ; B plays against C , D , and F ; C plays against every team except F ; D plays against every team except A ; E plays against every team except B ; and F plays against every team except C . Draw a graph that models the tournament.
Solution Summary: The author describes the required graph to model the given street-routing problem.
Six teams
(
A
,
B
,
C
,
D
,
E
,
and
F
)
are entered in a softball tournament. The top two seeded teams
(
A
and
B
)
have to play only three games; the other teams have to play four games each. The tournament pairings are
A
plays against
C
,
E
, and
F
;
B
plays against
C
,
D
, and
F
;
C
plays against every team except
F
;
D
plays against every team except
A
;
E
plays against every team except
B
; and
F
plays against every team except
C
. Draw a graph that models the tournament.
(4) (8 points)
(a) (2 points) Write down a normal vector n for the plane P given by the equation
x+2y+z+4=0.
(b) (4 points) Find two vectors v, w in the plane P that are not parallel.
(c) (2 points) Using your answers to part (b), write down a parametrization r: R² —
R3 of the plane P.
(2) (8 points) Determine normal vectors for the planes given by the equations x-y+2z = 3
and 2x + z = 3. Then determine a parametrization of the intersection line of the two
planes.
(3) (6 points)
(a) (4 points) Find all vectors u in the yz-plane that have magnitude [u
also are at a 45° angle with the vector j = (0, 1,0).
= 1 and
(b) (2 points) Using the vector u from part (a) that is counterclockwise to j, find an
equation of the plane through (0,0,0) that has u as its normal.
Chapter 5 Solutions
Excursions in Modern Mathematics, Books a la carte edition (9th Edition)
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