Mark, Tim, Maia, and Kelly are dividing among themselves a set of common assets equally owned by the four of them. The assets are divided into four shares ( s 1 , s 2 , s 3 and s 4 ) . Table 3 − 15 _ shows the values of the shares to each player expressed as a percent of the total value of the assets. T a b l e 3 − 1 5 s 1 s 2 s 3 s 4 Mark 20% 32% 28% 20% Tim 25% 25% 25% 25% Maia 15% 15% 30% 40% Kelly 24% 26% 24% 26% a. Which of the shares are fair shares to Mark? b. Which of the shares are fair shares to Tim? c. Which of the shares are fair shares to Maia? d. Which of the shares are fair shares to Kelly? e. Find all possible fair divisions of the assets using s 1 , s 2 , s 3 , and s 4 as shares.
Mark, Tim, Maia, and Kelly are dividing among themselves a set of common assets equally owned by the four of them. The assets are divided into four shares ( s 1 , s 2 , s 3 and s 4 ) . Table 3 − 15 _ shows the values of the shares to each player expressed as a percent of the total value of the assets. T a b l e 3 − 1 5 s 1 s 2 s 3 s 4 Mark 20% 32% 28% 20% Tim 25% 25% 25% 25% Maia 15% 15% 30% 40% Kelly 24% 26% 24% 26% a. Which of the shares are fair shares to Mark? b. Which of the shares are fair shares to Tim? c. Which of the shares are fair shares to Maia? d. Which of the shares are fair shares to Kelly? e. Find all possible fair divisions of the assets using s 1 , s 2 , s 3 , and s 4 as shares.
Solution Summary: The author explains how to find fair shares for Mark from the given table.
Mark, Tim, Maia, and Kelly are dividing among themselves a set of common assets equally owned by the four of them. The assets are divided into four shares
(
s
1
,
s
2
,
s
3
and
s
4
)
.
Table
3
−
15
_
shows the values of the shares to each player expressed as a percent of the total value of the assets.
T
a
b
l
e
3
−
1
5
s
1
s
2
s
3
s
4
Mark
20%
32%
28%
20%
Tim
25%
25%
25%
25%
Maia
15%
15%
30%
40%
Kelly
24%
26%
24%
26%
a. Which of the shares are fair shares to Mark?
b. Which of the shares are fair shares to Tim?
c. Which of the shares are fair shares to Maia?
d. Which of the shares are fair shares to Kelly?
e. Find all possible fair divisions of the assets using
s
1
,
s
2
,
s
3
, and
s
4
as shares.
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a.
f(x) = (x + 4x4) 5,
a = -1
lim f(x)
X--1
=
lim
x+4x
X--1
lim
X-1
4
x+4x
5
))"
5
))
by the power law
by the sum law
lim (x) + lim
X--1
4
4x
X-1
-(0,00+(
Find f(-1).
f(-1)=243
lim (x) +
-1 +4
35
4 ([
)
lim (x4)
5
x-1
Thus, by the definition of continuity, f is continuous at a = -1.
by the multiple constant law
by the direct substitution property
4 Use Cramer's rule to solve for x and t in the Lorentz-Einstein equations of special relativity:x^(')=\gamma (x-vt)t^(')=\gamma (t-v(x)/(c^(2)))where \gamma ^(2)(1-(v^(2))/(c^(2)))=1.
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