EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 38, Problem 18AR
To determine
(a)
The measurement on micrometer scale in part (a).
To determine
(b)
The measurement on micrometer scale in part (b).
To determine
(c)
The measurement on micrometer scale in part (c).
To determine
(d)
The measurement on micrometer scale in part (d).
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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
You recieve a case of fresh Michigan cherries that weighs 8.2 kg. You will be making cherry pies. Each pie will require 1 3/4 pounds of pitted cherries. How many pies can be made from the case if the yield percent for cherries is 87
Chapter 38 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 38 - Prob. 1ARCh. 38 - Holes are to be drilled in the length of angle...Ch. 38 - Prob. 3ARCh. 38 - Prob. 4ARCh. 38 - For each of the exercises in the following table,...Ch. 38 - Prob. 6ARCh. 38 - Prob. 7ARCh. 38 - Prob. 8ARCh. 38 - The following problems require computations with...Ch. 38 - Prob. 10AR
Ch. 38 - Read measurements a-h on the enlarged 32nds and...Ch. 38 - Prob. 12ARCh. 38 - Prob. 13ARCh. 38 - Read measurements i-p on the enlarged 50ths and...Ch. 38 - Prob. 15ARCh. 38 - Prob. 16ARCh. 38 - Read the vernier caliper and height gage...Ch. 38 - Prob. 18ARCh. 38 - Prob. 19ARCh. 38 - Prob. 20ARCh. 38 - Prob. 21AR
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