EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 29, Problem 12A
To determine
(a)
The main scale settings.
The verneir scale setting.
To determine
(b)
The main scale settings.
The verneir scale setting.
To determine
(c)
The main scale settings.
The verneir scale setting.
To determine
(d)
The main scale settings.
The verneir scale setting.
To determine
(e)
The main scale setting are
The verneir scale setting is
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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
Q/ show that the system:
x = Y + x(x² + y²)
y° =
=x+y (x² + y²)
9
X=-x(x²+ y²)
9 X
Y° = x - y (x² + y²)
have the same lin car part at (0,0) but they are topologically
different. Give the reason.
Chapter 29 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 29 - Measure this line segment to the nearest 164.Ch. 29 - A hole has a diameter of 13.741 mm 0.002mm+0.005mm...Ch. 29 - For the measurement 74.38 mm, find (a) the degree...Ch. 29 - Express 87.6 inches as feet.Ch. 29 - If 1450 parts can be produced in 15.35 hours, how...Ch. 29 - Prob. 6ACh. 29 - Prob. 7ACh. 29 - Prob. 8ACh. 29 - Prob. 9ACh. 29 - Prob. 10A
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