Pearson eText for Business Math -- Instant Access (Pearson+)
11th Edition
ISBN: 9780137518883
Author: Cheryl Cleaves, Margie Hobbs
Publisher: PEARSON+
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Chapter 14, Problem 19ES
To determine
To calculate: The amount that needs to be invested today to get the following stream of payments in the annuity liquidation phase,
| Payment amount | Annual Interest rate | Years | Frequency of Payments |
| $5,000 | 8% | 4 | Quarterly |
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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
2. If loga b + log, a = √√29, find all possible values of loga blog, a
I need some assistance solving Part B of this question. Refer to the excel data in the image provided to answer Part B. SoftBus Company sells PC equipment and customized software to small companies to help them manage their day-to-day business activities. Although SoftBus spends time with all customers to understand their needs, the customers are eventually on their own to use the equipment and software intelligently. To understand its customers better, SoftBus recently sent questionnaires to a large number of prospective customers. Key personnel—those who would be using the software—were asked to fill out the questionnaire. SoftBus received 82 usable responses, as shown in the file. You can assume that these employees represent a random sample of all of SoftBus's prospective customers. SoftBus believes it can afford to spend much less time with customers who own PCs and score at least 4 on PC Knowledge. Let's call these the "PC-savvy" customers. On the other hand, SoftBus believes it…
Chapter 14 Solutions
Pearson eText for Business Math -- Instant Access (Pearson+)
Ch. 14.1 - Prob. 1-1SCCh. 14.1 - Prob. 1-2SCCh. 14.1 - Prob. 1-3SCCh. 14.1 - Prob. 1-4SCCh. 14.1 - Prob. 2-1SCCh. 14.1 - Prob. 2-2SCCh. 14.1 - Prob. 2-3SCCh. 14.1 - Prob. 2-4SCCh. 14.1 - Prob. 2-5SCCh. 14.1 - Prob. 2-6SC
Ch. 14.1 - Prob. 3-1SCCh. 14.1 - Prob. 3-2SCCh. 14.1 - Prob. 3-3SCCh. 14.1 - Prob. 3-4SCCh. 14.1 - Prob. 4-1SCCh. 14.1 - Prob. 4-2SCCh. 14.1 - Prob. 4-3SCCh. 14.1 - Prob. 4-4SCCh. 14.1 - Prob. 5-1SCCh. 14.1 - Prob. 5-2SCCh. 14.1 - Prob. 5-3SCCh. 14.1 - Prob. 5-4SCCh. 14.1 - Prob. 6-1SCCh. 14.1 - Prob. 6-2SCCh. 14.1 - Prob. 6-3SCCh. 14.1 - Prob. 6-4SCCh. 14.1 - Prob. 6-5SCCh. 14.1 - Prob. 6-6SCCh. 14.1 - Prob. 1SECh. 14.1 - Prob. 2SECh. 14.1 - Prob. 3SECh. 14.1 - Prob. 4SECh. 14.1 - Prob. 5SECh. 14.1 - Prob. 6SECh. 14.1 - Prob. 7SECh. 14.1 - Prob. 8SECh. 14.1 - Prob. 9SECh. 14.1 - Prob. 10SECh. 14.1 - Prob. 11SECh. 14.1 - Prob. 12SECh. 14.1 - Prob. 13SECh. 14.1 - Prob. 14SECh. 14.1 - Prob. 15SECh. 14.1 - Prob. 16SECh. 14.1 - Prob. 17SECh. 14.1 - Prob. 18SECh. 14.1 - Prob. 19SECh. 14.1 - Prob. 20SECh. 14.1 - Prob. 21SECh. 14.1 - Prob. 22SECh. 14.1 - Prob. 23SECh. 14.1 - Prob. 24SECh. 14.1 - Prob. 25SECh. 14.1 - Prob. 26SECh. 14.1 - Prob. 27SECh. 14.1 - Prob. 28SECh. 14.1 - Prob. 29SECh. 14.1 - Prob. 30SECh. 14.2 - Prob. 1-1SCCh. 14.2 - Prob. 1-2SCCh. 14.2 - Prob. 1-3SCCh. 14.2 - Prob. 1-4SCCh. 14.2 - Prob. 2-1SCCh. 14.2 - Prob. 2-2SCCh. 14.2 - Prob. 2-3SCCh. 14.2 - Prob. 2-4SCCh. 14.2 - Prob. 3-1SCCh. 14.2 - Prob. 3-2SCCh. 14.2 - Prob. 1SECh. 14.2 - Prob. 2SECh. 14.2 - Prob. 3SECh. 14.2 - Prob. 4SECh. 14.2 - Prob. 5SECh. 14.2 - Prob. 6SECh. 14.2 - Prob. 7SECh. 14.2 - Prob. 8SECh. 14.2 - Prob. 9SECh. 14.2 - Prob. 10SECh. 14.2 - Prob. 11SECh. 14.2 - Prob. 12SECh. 14.2 - Prob. 13SECh. 14.2 - Prob. 14SECh. 14 - Prob. 1ESCh. 14 - Prob. 2ESCh. 14 - Prob. 3ESCh. 14 - Prob. 4ESCh. 14 - Prob. 5ESCh. 14 - Prob. 6ESCh. 14 - Prob. 7ESCh. 14 - Prob. 8ESCh. 14 - Prob. 9ESCh. 14 - Prob. 10ESCh. 14 - Prob. 11ESCh. 14 - Prob. 12ESCh. 14 - Prob. 13ESCh. 14 - Prob. 14ESCh. 14 - Prob. 15ESCh. 14 - Prob. 16ESCh. 14 - Prob. 17ESCh. 14 - Prob. 18ESCh. 14 - Prob. 19ESCh. 14 - Prob. 20ESCh. 14 - Prob. 21ESCh. 14 - Prob. 22ESCh. 14 - Prob. 23ESCh. 14 - Prob. 24ESCh. 14 - Prob. 25ESCh. 14 - Prob. 26ESCh. 14 - Prob. 27ESCh. 14 - Prob. 28ESCh. 14 - Prob. 29ESCh. 14 - Prob. 30ESCh. 14 - Prob. 31ESCh. 14 - Prob. 32ESCh. 14 - Prob. 33ESCh. 14 - Prob. 34ESCh. 14 - Prob. 35ESCh. 14 - Prob. 36ESCh. 14 - Prob. 37ESCh. 14 - Prob. 38ESCh. 14 - Prob. 39ESCh. 14 - Prob. 1PTCh. 14 - Prob. 2PTCh. 14 - Prob. 3PTCh. 14 - Prob. 4PTCh. 14 - Prob. 5PTCh. 14 - Prob. 6PTCh. 14 - Prob. 7PTCh. 14 - Prob. 8PTCh. 14 - Prob. 9PTCh. 14 - Prob. 10PTCh. 14 - Prob. 11PTCh. 14 - Prob. 12PTCh. 14 - Prob. 13PTCh. 14 - Prob. 14PTCh. 14 - Prob. 15PTCh. 14 - Prob. 16PTCh. 14 - Prob. 17PTCh. 14 - Prob. 18PTCh. 14 - Prob. 19PTCh. 14 - Prob. 20PTCh. 14 - Prob. 21PTCh. 14 - Prob. 22PTCh. 14 - Prob. 23PTCh. 14 - Prob. 24PTCh. 14 - Prob. 25PTCh. 14 - Prob. 1CTCh. 14 - Prob. 2CTCh. 14 - Prob. 3CTCh. 14 - Prob. 4CTCh. 14 - Prob. 5CTCh. 14 - Prob. 6CTCh. 14 - Prob. 7CTCh. 14 - Prob. 8CTCh. 14 - Prob. 9CTCh. 14 - Prob. 10CTCh. 14 - Prob. 1CPCh. 14 - Prob. 2CPCh. 14 - Prob. 3CPCh. 14 - Prob. 1CS1Ch. 14 - Prob. 2CS1Ch. 14 - Prob. 3CS1Ch. 14 - Prob. 4CS1Ch. 14 - Prob. 5CS1Ch. 14 - Prob. 1CS2Ch. 14 - Prob. 2CS2Ch. 14 - Prob. 3CS2Ch. 14 - Prob. 4CS2Ch. 14 - Prob. 5CS2Ch. 14 - Prob. 1CS3Ch. 14 - Prob. 2CS3Ch. 14 - Prob. 3CS3Ch. 14 - Prob. 4CS3Ch. 14 - Prob. 5CS3Ch. 14 - Prob. 6CS3
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