Exercise 35 through 38 refer to the following situation: Angela, Boris, and Carlos are dividing the vanilla-strawberry cake shown in Fig.3-23(a) using the lone-chooser method. Fig.3-23(b) shows how each player values each half of the cake. In your answers assume that all cuts are normal “cake cuts” from the center to the edge of the cake. You can describe each piece of cake by giving the angles of the vanilla and strawberry parts, as in “
Suppose that Angela and Boris are the dividers and Carlos is the chooser. In the first division, Boris cuts the cake vertically through the center as shown in Fig.3-24, with Angela choosing
a. Describe how Angela would subdivide
b. Describe how Boris would subdivide
c. Based on the subdivisions in (a) and (b), describe a possible final fair division of the cake.
d. For the final fair division you described in (c), find the value (in dollars and cents) of each share in the eyes of the player receiving it.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Student's Solutions Manual For Excursions In Modern Mathematics Format: Paperback
- What relationship, if any, exists between two angles a with equal measures? b that have the same vertex and a common side between them?arrow_forwardFor Exercises 11 and 12, use the drawing provided. If AB=11.8andAX=6.9, find XBarrow_forwardUse theorem 5.4.3 to form a proportion in which RS is a geometric mean. Hint RVSRST Exercises 1-6arrow_forward
- Given the points A(-3, -4) and B(2, 0), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2 to 3.arrow_forwardshow corresponding sides are in proportion in order to prove the side splitter theorem.arrow_forwardIf x, y, and z are lengths of the edges of a rectangular box, the common length of the box's diagonals is s=arrow_forward
- Given the directed line segment , Find the coordinates of P, such that P is the point partitioning n the ratio 3:2arrow_forwardIf m<LMK = (6a + 18)°, find a so that ML intersects MK.arrow_forwardWhich of the following is always true about the lengths of the SHD and SD of skew lines? Choose the best answer. a. Shortest Horizontal Distance > Shortest Distance b. Shortest Horizontal Distance not equal to Shortest Distance c. Shortest Horizontal Distance >= Shortest Distance d. Shortest Horizontal Distance <= Shortest Distance e. Shortest Horizontal Distance < Shortest Distance f. Shortest Horizontal Distance = Shortest Distancearrow_forward
- 1) What is the ordered pair for point E in rectangle CDEF in terms of “a” and/or “b”?arrow_forwardGiven the point A(-3, -2) and B(6, 1), find the coordinates of the point P on directed line segment BA that partition BA in the ratio 3:1.arrow_forwardUsing Definition II and Figure 9, we would refer to a as the side _________ A, b asthe side __________ to A, and c as the ____________.arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,