EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 46, Problem 6A
To determine
To read the metric height gage measurement for the given setting.
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Good Day, Please assist with this query.
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 46 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 46 - Solve x3=15.Express the answer as both a common...Ch. 46 - Solve the equation 75.4=5.2C for the unknown value...Ch. 46 - Find the unknown value of b in the equation...Ch. 46 - Prob. 4ACh. 46 - Prob. 5ACh. 46 - Prob. 6ACh. 46 - Prob. 7ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 9ACh. 46 - Solve for the unknown and check each of the...
Ch. 46 - Prob. 11ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 13ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 15ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 17ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 25ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 27ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 29ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 33ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - Prob. 35ACh. 46 - Solve for the unknown and check each of the...Ch. 46 - The following formulas are used in the machine...Ch. 46 - The following formulas are used in the machine...Ch. 46 - Prob. 39ACh. 46 - The following formulas are used in the machine...Ch. 46 - Prob. 41ACh. 46 - The following formulas are used in the machine...Ch. 46 - Prob. 43ACh. 46 - The following formulas are used in the machine...Ch. 46 - Prob. 45ACh. 46 - The following formulas are used in the machine...Ch. 46 - Prob. 47ACh. 46 - The following formulas are used in the machine...Ch. 46 - Prob. 49ACh. 46 - The following formulas are used in the machine...Ch. 46 - Prob. 51ACh. 46 - The following formulas are used in machine trade...Ch. 46 - Prob. 53ACh. 46 - The following formulas are used in machine trade...Ch. 46 - Prob. 55ACh. 46 - Prob. 56ACh. 46 - Prob. 57ACh. 46 - The following formulas are used in machine trade...Ch. 46 - Prob. 59ACh. 46 - For applications 60 and 61, rearrange each formula...Ch. 46 - Prob. 61ACh. 46 - Solve for the unknown value in each of the...Ch. 46 - Prob. 63ACh. 46 - Solve for the unknown value in each of the...Ch. 46 - Prob. 65ACh. 46 - Solve for the unknown value in each of the...Ch. 46 - Prob. 67ACh. 46 - Prob. 68ACh. 46 - Prob. 69ACh. 46 - Solve for the unknown value in each of the...Ch. 46 - Prob. 71ACh. 46 - Solve for the unknown value in each of the...Ch. 46 - Prob. 73ACh. 46 - Solve for the unknown value in each of the...Ch. 46 - Prob. 75A
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- 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.arrow_forwardQ/ 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_forward
- 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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