
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 82, Problem 25A
To determine
Convert the binary number
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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 82 Solutions
Mathematics for Machine Technology
Ch. 82 - Prob. 1ACh. 82 - Prob. 2ACh. 82 - Prob. 3ACh. 82 - Prob. 4ACh. 82 - Prob. 5ACh. 82 - Prob. 6ACh. 82 - Prob. 7ACh. 82 - Prob. 8ACh. 82 - Prob. 9ACh. 82 - Analyze the following numbers. 0.802
Ch. 82 - Prob. 11ACh. 82 - Prob. 12ACh. 82 - Prob. 13ACh. 82 - Prob. 14ACh. 82 - Prob. 15ACh. 82 - Prob. 16ACh. 82 - Prob. 17ACh. 82 - Prob. 18ACh. 82 - Prob. 19ACh. 82 - Prob. 20ACh. 82 - Prob. 21ACh. 82 - Prob. 22ACh. 82 - Prob. 23ACh. 82 - Prob. 24ACh. 82 - Prob. 25ACh. 82 - Prob. 26ACh. 82 - Prob. 27ACh. 82 - Prob. 28ACh. 82 - Prob. 29ACh. 82 - Prob. 30ACh. 82 - Prob. 31ACh. 82 - Prob. 32ACh. 82 - Prob. 33ACh. 82 - Prob. 34ACh. 82 - Prob. 35ACh. 82 - Express the following binary numbers as decimal...Ch. 82 - Prob. 37ACh. 82 - Prob. 38ACh. 82 - Prob. 39ACh. 82 - Prob. 40ACh. 82 - Prob. 41ACh. 82 - Prob. 42ACh. 82 - Prob. 43ACh. 82 - Prob. 44ACh. 82 - Prob. 45ACh. 82 - Prob. 46ACh. 82 - Prob. 47ACh. 82 - Prob. 48ACh. 82 - Prob. 49ACh. 82 - Prob. 50ACh. 82 - Prob. 51ACh. 82 - Prob. 52ACh. 82 - Express the following decimal numbers as binary...Ch. 82 - Prob. 54ACh. 82 - Prob. 55ACh. 82 - Prob. 56ACh. 82 - Express the following decimal numbers as binary...
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- A: Show that the ODES has no limit cycle in a region D and find this region: x=y-2x³ y=x+y-2y3 Carrow_forwardoptımızatıon theoryarrow_forwardQ3)A: Given H(x,y)= x²-x4 + y² as a first integral of an ODEs, find this ODES corresponding to H(x,y) and show the phase portrait by using Hartman theorem and by drawing graph of H(x,y)=c. Discuss the stability of critical points of the corresponding ODEs.arrow_forward
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