Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 17, Problem 8AR
To determine
(a)
To evaluate the given expression.
To determine
(b)
To find the simplified value given expression.
To determine
(c)
To evaluate the given expression.
To determine
(d)
To find the simplified value of given fractions.
To determine
(e)
To evaluate the given expression.
To determine
(f)
To evaluate the given expression.
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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 17 Solutions
Mathematics for Machine Technology
Ch. 17 - Express each of the following fractions as...Ch. 17 - Prob. 2ARCh. 17 - Prob. 3ARCh. 17 - Prob. 4ARCh. 17 - Prob. 5ARCh. 17 - Prob. 6ARCh. 17 - Prob. 7ARCh. 17 - Prob. 8ARCh. 17 - How many complete pieces can be blanked from a...Ch. 17 - How many inches of bar stock are needed to make 30...
Ch. 17 - A shaft is turned at 200 per minute with a tool...Ch. 17 - A shop order calls for 1800 steel pins each...Ch. 17 - Prob. 13ARCh. 17 - Write each of the following numbers as words. a....Ch. 17 - Prob. 15ARCh. 17 - Round each of the following numbers to the...Ch. 17 - Prob. 17ARCh. 17 - Prob. 18ARCh. 17 - Prob. 19ARCh. 17 - Prob. 20ARCh. 17 - Raise each of the following values to the...Ch. 17 - Determine the roots of each of the following...Ch. 17 - Prob. 23ARCh. 17 - Find the decimal or fraction equivalents of each...Ch. 17 - Determine the nearer fractional equivalents of...Ch. 17 - Solve each of the following combined operations...Ch. 17 - Prob. 27ARCh. 17 - A combination of gage Nocks is selected to provide...Ch. 17 - A piece of round stock is being turned to a...Ch. 17 - A plate 57.20 millimeters thick is to be machined...Ch. 17 - A shaft is turned in a lathe at 120 revolutions...
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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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