Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices ( s 1 , s 2 , s 3 , s 4 , s 5 ) the choosers C 1 , C 2 , C 3 , and C 4 submit their bids for these shares. a. Suppose that the choosers’ bid lists are C 1 : { s 2 , s 3 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 1 , s 2 } ; C 4 : { s 1 , s 3 , s 4 } Describe three different fair divisions of the land. Explain why that’s it—why there are no others. b. Suppose that the choosers bid lists are C 1 : { s 1 , s 4 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 2 , s 4 , s 5 } ; C 4 : { s 2 } Find a fair division of the cake. Explain why that’s it—there are no others.
Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices ( s 1 , s 2 , s 3 , s 4 , s 5 ) the choosers C 1 , C 2 , C 3 , and C 4 submit their bids for these shares. a. Suppose that the choosers’ bid lists are C 1 : { s 2 , s 3 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 1 , s 2 } ; C 4 : { s 1 , s 3 , s 4 } Describe three different fair divisions of the land. Explain why that’s it—why there are no others. b. Suppose that the choosers bid lists are C 1 : { s 1 , s 4 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 2 , s 4 , s 5 } ; C 4 : { s 2 } Find a fair division of the cake. Explain why that’s it—there are no others.
Solution Summary: The author explains the three fair divisions of the land using the lone-divider method.
Five players are dividing a cake among themselves using the lone-divider method. After the divider
D
cuts the cake into five slices
(
s
1
,
s
2
,
s
3
,
s
4
,
s
5
)
the choosers
C
1
,
C
2
,
C
3
, and
C
4
submit their bids for these shares.
a. Suppose that the choosers’ bid lists are
C
1
:
{
s
2
,
s
3
}
;
C
2
:
{
s
2
,
s
4
}
;
C
3
:
{
s
1
,
s
2
}
;
C
4
:
{
s
1
,
s
3
,
s
4
}
Describe three different fair divisions of the land. Explain why that’s it—why there are no others.
b. Suppose that the choosers bid lists are
C
1
:
{
s
1
,
s
4
}
;
C
2
:
{
s
2
,
s
4
}
;
C
3
:
{
s
2
,
s
4
,
s
5
}
;
C
4
:
{
s
2
}
Find a fair division of the cake. Explain why that’s it—there are no others.
A boat is 15 ft away from a point perpendicular to the shoreline. A
person stands at a point down the shoreline so that a 65° angle
is formed between the closest point to the boat, the person, and
the boat. How far is the person from the boat? Round your
answer to the nearest tenth of a foot. Show your work.
boat
15 ft
d
65°
person
2. Find the value of x in the triangle. Round your answer to the
nearest tenth of a degree. Show your work.
8
15
Use the equation x+2= √3x+10 to answer these questions.
(a) What is the solution to the equation?
(b) What is the extraneous solution? Why?
(c) In general, what is an extraneous solution?
Chapter 3 Solutions
Excursions in Mathematics, Loose-Leaf Edition Plus MyLab Math with Pearson eText -- 18 Week Access Card Package
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning