
Business Math (11th Edition)
11th Edition
ISBN: 9780134496436
Author: Cheryl Cleaves, Margie Hobbs, Jeffrey Noble
Publisher: PEARSON
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Question
Chapter 20, Problem 4CS2
To determine
The best job for Rita whether inPennsylvania or Maryland when the federal income taxes due in Pennsylvaniaand Maryland is $7,925 and $10,025 respectively and the base wages are $55,000 and $65,000 respectively. Also, she needs to pay additional taxes of amount $2,836.25 if she moved to Maryland and she received amount of $5,000 as a sign in bonus in Pennsylvania, provided that the average rate of state income tax is 3%.
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1. Find the solution set of In(x) sin(x) ≤ 0, for x = [0,14].
Suppose you are gambling on a roulette wheel. Each time the wheel is spun, the result is one of the outcomes 0, 1, and so on through 36. Of these outcomes, 18 are red, 18 are black, and 1 is green. On each spin you bet $5 that a red outcome will occur and $1 that the green outcome will occur. If red occurs, you win a net $4. (You win $10 from red and nothing from green.) If green occurs, you win a net $24. (You win $30 from green and nothing from red.) If black occurs, you lose everything you bet for a loss of $6.
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4. Consider Chebychev's equation
(1 - x²)y" - xy + λy = 0
with boundary conditions y(-1) = 0 and y(1) = 0, where X is a constant.
(a) Show that Chebychev's equation can be expressed in Sturm-Liouville form
d
· (py') + qy + Ary = 0,
dx
y(1) = 0, y(-1) = 0,
where p(x) = (1 = x²) 1/2, q(x) = 0 and r(x) = (1 − x²)-1/2
(b) Show that the eigenfunctions of the Sturm-Liouville equation are extremals of the
functional A[y], where
A[y]
=
I[y]
J[y]'
and I[y] and [y] are defined by
-
I [y] = √, (my² — qy²) dx
and
J[y] = [[", ry² dx.
Explain briefly how to use this to obtain estimates of the smallest eigenvalue >1.
1
(c) Let k > be a parameter. Explain why the functions y(x) = (1-x²) are suitable
4
trial functions for estimating the smallest eigenvalue. Show that the value of A[y]
for these trial functions is
4k2
A[y] =
=
4k - 1'
and use this to estimate the smallest eigenvalue \1.
Hint:
L₁ x²(1 − ²)³¹ dr =
1
(1 - x²)³ dx
(ẞ > 0).
2ẞ
Chapter 20 Solutions
Business Math (11th Edition)
Ch. 20.1 - Prob. 1-1SCCh. 20.1 - Prob. 1-2SCCh. 20.1 - Prob. 1-3SCCh. 20.1 - Prob. 1-4SCCh. 20.1 - Prob. 1-5SCCh. 20.1 - Prob. 1-6SCCh. 20.1 - Prob. 2-1SCCh. 20.1 - Prob. 2-2SCCh. 20.1 - Prob. 2-3SCCh. 20.1 - Prob. 2-4SC
Ch. 20.1 - Prob. 1SECh. 20.1 - Prob. 2SECh. 20.1 - Prob. 3SECh. 20.1 - Prob. 4SECh. 20.1 - Prob. 5SECh. 20.1 - Prob. 6SECh. 20.1 - Prob. 7SECh. 20.1 - Prob. 8SECh. 20.1 - Prob. 9SECh. 20.1 - Prob. 10SECh. 20.1 - Prob. 11SECh. 20.1 - Prob. 12SECh. 20.1 - Prob. 13SECh. 20.1 - Prob. 14SECh. 20.1 - Prob. 15SECh. 20.1 - Prob. 16SECh. 20.1 - Prob. 17SECh. 20.1 - Prob. 18SECh. 20.1 - Prob. 19SECh. 20.1 - Prob. 20SECh. 20.2 - Prob. 1-1SCCh. 20.2 - Prob. 1-2SCCh. 20.2 - Prob. 1-3SCCh. 20.2 - Prob. 1-4SCCh. 20.2 - Prob. 2-1SCCh. 20.2 - Prob. 2-2SCCh. 20.2 - Prob. 2-3SCCh. 20.2 - Prob. 2-4SCCh. 20.2 - Prob. 3-1SCCh. 20.2 - Prob. 3-2SCCh. 20.2 - Prob. 3-3SCCh. 20.2 - Prob. 3-4SCCh. 20.2 - Prob. 3-5SCCh. 20.2 - Prob. 3-6SCCh. 20.2 - Prob. 1SECh. 20.2 - Prob. 2SECh. 20.2 - Prob. 3SECh. 20.2 - Prob. 4SECh. 20.2 - Prob. 5SECh. 20.2 - Prob. 6SECh. 20.2 - Prob. 7SECh. 20.2 - Prob. 8SECh. 20.2 - Prob. 9SECh. 20.2 - Prob. 10SECh. 20.2 - Prob. 11SECh. 20.2 - Prob. 12SECh. 20.2 - Prob. 13SECh. 20.2 - Prob. 14SECh. 20.2 - Prob. 15SECh. 20.2 - Prob. 16SECh. 20.2 - Prob. 17SECh. 20.2 - Prob. 18SECh. 20.2 - Prob. 19SECh. 20.2 - Prob. 20SECh. 20.2 - Prob. 21SECh. 20.2 - Prob. 22SECh. 20.2 - Prob. 23SECh. 20.3 - Prob. 1-1SCCh. 20.3 - Prob. 1-2SCCh. 20.3 - Prob. 1-3SCCh. 20.3 - Prob. 1-4SCCh. 20.3 - Prob. 2-1SCCh. 20.3 - Prob. 2-2SCCh. 20.3 - Prob. 2-3SCCh. 20.3 - Prob. 2-4SCCh. 20.3 - Prob. 3-1SCCh. 20.3 - Prob. 3-2SCCh. 20.3 - Prob. 3-3SCCh. 20.3 - Prob. 3-4SCCh. 20.3 - Prob. 1SECh. 20.3 - Prob. 2SECh. 20.3 - Prob. 3SECh. 20.3 - Prob. 4SECh. 20.3 - Prob. 5SECh. 20.3 - Prob. 6SECh. 20.3 - Prob. 7SECh. 20.3 - Prob. 8SECh. 20.3 - Prob. 9SECh. 20.3 - Prob. 10SECh. 20.3 - Prob. 11SECh. 20.3 - Prob. 12SECh. 20.3 - Prob. 13SECh. 20.3 - Prob. 14SECh. 20.3 - Prob. 15SECh. 20.3 - Prob. 16SECh. 20.3 - Prob. 17SECh. 20.3 - Prob. 18SECh. 20.3 - Prob. 19SECh. 20.3 - Prob. 20SECh. 20 - Prob. 1ESCh. 20 - Prob. 2ESCh. 20 - Prob. 3ESCh. 20 - Prob. 4ESCh. 20 - Prob. 5ESCh. 20 - Prob. 6ESCh. 20 - Prob. 7ESCh. 20 - Prob. 8ESCh. 20 - Prob. 9ESCh. 20 - Prob. 10ESCh. 20 - Prob. 11ESCh. 20 - Prob. 12ESCh. 20 - Prob. 13ESCh. 20 - Prob. 14ESCh. 20 - Prob. 15ESCh. 20 - Prob. 16ESCh. 20 - Prob. 17ESCh. 20 - Prob. 18ESCh. 20 - Prob. 19ESCh. 20 - Prob. 20ESCh. 20 - Prob. 21ESCh. 20 - Prob. 22ESCh. 20 - Prob. 23ESCh. 20 - Prob. 24ESCh. 20 - Prob. 25ESCh. 20 - Prob. 26ESCh. 20 - Prob. 27ESCh. 20 - Prob. 28ESCh. 20 - Prob. 29ESCh. 20 - Prob. 30ESCh. 20 - Prob. 31ESCh. 20 - Prob. 32ESCh. 20 - Prob. 33ESCh. 20 - Prob. 34ESCh. 20 - Prob. 35ESCh. 20 - Prob. 36ESCh. 20 - Prob. 37ESCh. 20 - Prob. 38ESCh. 20 - Prob. 39ESCh. 20 - Prob. 40ESCh. 20 - Prob. 41ESCh. 20 - Prob. 42ESCh. 20 - Prob. 43ESCh. 20 - Prob. 44ESCh. 20 - Prob. 45ESCh. 20 - Prob. 46ESCh. 20 - Prob. 47ESCh. 20 - Prob. 48ESCh. 20 - Prob. 49ESCh. 20 - Prob. 50ESCh. 20 - Prob. 51ESCh. 20 - Prob. 52ESCh. 20 - Prob. 53ESCh. 20 - Prob. 54ESCh. 20 - Prob. 55ESCh. 20 - Prob. 56ESCh. 20 - Prob. 57ESCh. 20 - Prob. 58ESCh. 20 - Prob. 59ESCh. 20 - Prob. 60ESCh. 20 - Prob. 61ESCh. 20 - Prob. 62ESCh. 20 - Prob. 63ESCh. 20 - Prob. 64ESCh. 20 - Prob. 65ESCh. 20 - Prob. 66ESCh. 20 - Prob. 67ESCh. 20 - Prob. 68ESCh. 20 - Prob. 69ESCh. 20 - Prob. 70ESCh. 20 - Prob. 71ESCh. 20 - Prob. 72ESCh. 20 - Prob. 1PTCh. 20 - Prob. 2PTCh. 20 - Prob. 3PTCh. 20 - Prob. 4PTCh. 20 - Prob. 5PTCh. 20 - Prob. 6PTCh. 20 - Prob. 7PTCh. 20 - Prob. 8PTCh. 20 - Prob. 9PTCh. 20 - Prob. 10PTCh. 20 - Prob. 11PTCh. 20 - Prob. 12PTCh. 20 - Prob. 13PTCh. 20 - Prob. 14PTCh. 20 - Prob. 15PTCh. 20 - Prob. 16PTCh. 20 - Prob. 17PTCh. 20 - Prob. 18PTCh. 20 - Prob. 19PTCh. 20 - Prob. 20PTCh. 20 - Prob. 21PTCh. 20 - Prob. 22PTCh. 20 - Prob. 1CTCh. 20 - Prob. 2CTCh. 20 - Prob. 3CTCh. 20 - Prob. 4CTCh. 20 - Prob. 5CTCh. 20 - Prob. 6CTCh. 20 - Prob. 7CTCh. 20 - Prob. 8CTCh. 20 - Prob. 1CPCh. 20 - Prob. 2CPCh. 20 - Prob. 1CS1Ch. 20 - Prob. 2CS1Ch. 20 - Prob. 3CS1Ch. 20 - Prob. 4CS1Ch. 20 - Prob. 1CS2Ch. 20 - Prob. 2CS2Ch. 20 - Prob. 3CS2Ch. 20 - Prob. 4CS2
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