Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
expand_more
expand_more
format_list_bulleted
Question
Chapter 63, Problem 23A
To determine
The height of forging of a regular pyramid.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
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 63 Solutions
Mathematics For Machine Technology
Ch. 63 - A rectangular strip of steel 2 ft 4 in. long, 1 ft...Ch. 63 - In order to make a conical duct, a circular sheet...Ch. 63 - A square bar 78 in. on a side is to be milled from...Ch. 63 - Construct a regular hexagon 3 cm on a side. By...Ch. 63 - Two angles of a triangle measure 7318' and 4947'....Ch. 63 - Prob. 6ACh. 63 - Prob. 7ACh. 63 - Prob. 8ACh. 63 - Prob. 9ACh. 63 - Prob. 10A
Ch. 63 - Solve these exercises. Where necessary, round the...Ch. 63 - Prob. 12ACh. 63 - A vessel is in the shape of a right circular cone....Ch. 63 - Prob. 14ACh. 63 - Prob. 15ACh. 63 - A piece in the shape of a pyramid with a regular...Ch. 63 - Prob. 17ACh. 63 - Solve these exercises. Where necessary, round the...Ch. 63 - Prob. 19ACh. 63 - Prob. 20ACh. 63 - Prob. 21ACh. 63 - Solve these exercises. Where necessary, round the...Ch. 63 - Prob. 23ACh. 63 - Prob. 24ACh. 63 - Prob. 25ACh. 63 - The container is in the shape of a frustum of a...Ch. 63 - A steel forging is in the shape of a frustum of a...Ch. 63 - Find the volume of the frustum of a right circular...Ch. 63 - Prob. 29ACh. 63 - The side view of a tapered steel shaft is shown....Ch. 63 - A zinc casting is in the shape of a frustum of a...Ch. 63 - A piece in the shape of a frustum of a pyramid...Ch. 63 - Find the volume of a hollow machined steel piece...Ch. 63 - Prob. 34A
Knowledge Booster
Similar questions
- 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
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage, 
Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill