EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Question
Chapter 76, Problem 1A
To determine
To find the length of the diagonal
Expert Solution & Answer

Answer to Problem 1A
Explanation of Solution
Given information:
We are given the following figure-
Calculation:
After observing the figure closely and then writing the relation to calculate the length of diagonal
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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 76 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 76 - Prob. 1ACh. 76 - Prob. 2ACh. 76 - Prob. 3ACh. 76 - Prob. 4ACh. 76 - Prob. 5ACh. 76 - Prob. 6ACh. 76 - Prob. 7ACh. 76 - Prob. 8ACh. 76 - Prob. 9ACh. 76 - Prob. 10A
Ch. 76 - Prob. 11ACh. 76 - Prob. 12ACh. 76 - Prob. 13ACh. 76 - In each Exercises 13 through 16, the top, front,...Ch. 76 - In each Exercises 13 through 16, the top, front,...Ch. 76 - Prob. 16ACh. 76 - Prob. 17ACh. 76 - In each of the following exercises, the top,...Ch. 76 - Prob. 19ACh. 76 - Prob. 20ACh. 76 - Prob. 21ACh. 76 - Prob. 22A
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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
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