EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 25, Problem 8A
To determine
(a)
To convert given length as indicated length.
To determine
(b)
To convert given length as indicated length.
To determine
(c)
To convert given length as indicated length.
To determine
(d)
To convert given length as indicated length.
To determine
(e)
To convert given length as indicated length.
To determine
(f)
To convert given length as indicated length.
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Students have asked these similar questions
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 25 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
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- Q/ Find the region where ODES has no limit cycle: -X = X + X3 y=x+y+y'arrow_forwardB:Show that the function 4H(x,y)= (x² + y2)2-2((x² + y²) is a first integral of ODES: x=y + y(x² + y²) y=x+x (x² + y²) and sketch the stability of critical points and draw the phase portrait of system.arrow_forwardA: Show that the ODES has no limit cycle in a region D and find this region: x=y-2x³ y=x+y-2y3 Carrow_forward
- optımızatıon 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_forwardSolve the given differential equation by using an appropriate substitution. The DE is homogeneous. y-x dy dx = y + xarrow_forward
- Q1: solve the system y 2 In √√x² + y2 X y = −y + In √√x² + y2 and solve the linear part.arrow_forwardFind all the solutions of the congruence 7x² + 15x = 4 (mod 111).arrow_forward) The set {1,2,..., 22} is to be split into two disjoint non-empty sets S and T in such a way that: (i) the product (mod 23) of any two elements of S lies in S; (ii) the product (mod 23) of any two elements of T lies in S; (iii) the product (mod 23) of any element of S and any element of T lies in T. Prove that the only solution is S = {1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18}, T= {5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22}.arrow_forward
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