Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 62, Problem 18A
Solve these exercises.
A company produces spherical copper parts with 1.46-inch diameters. Each part weighs 0.523 pound. A larger spherical copper part 2.27 inches in diameter is planned. Determine the weight of the larger part. Round the answer to 2 decimal places.
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A surveyor sees a building across the river. Standing at point A he measures the angle of elevation
from the ground to the top of the building to be 30 degrees. He steps back 100 feet and again
measures the angle of elevation and finds it to be 15. (See Figure 12.26.) Assuming that it makes a
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Figure 12.26
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Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
AR and MA orders of this representation.
(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Chapter 62 Solutions
Mathematics for Machine Technology
Ch. 62 - In order to make a conical duct a circular sheet...Ch. 62 - Prob. 2ACh. 62 - Prob. 3ACh. 62 - Convert 12.02 sq in. to square centimeters.Ch. 62 - Prob. 5ACh. 62 - Prob. 6ACh. 62 - Prob. 7ACh. 62 - Compute the volume of each sphere 7 through 14....Ch. 62 - Prob. 9ACh. 62 - Compute the volume of each sphere 7 through 14....
Ch. 62 - Prob. 11ACh. 62 - Compute the volume of each sphere 7 through 14....Ch. 62 - Prob. 13ACh. 62 - Compute the volume of each sphere 7 through 14....Ch. 62 - Prob. 15ACh. 62 - Solve these exercise. A vat in the shape of a...Ch. 62 - Prob. 17ACh. 62 - Solve these exercises. A company produces...Ch. 62 - Solve these exercises. Pieces in the shape of...Ch. 62 - Solve these exercises. A plastic products...Ch. 62 - Solve these exercises. Find the weight of the...Ch. 62 - Compute the capacity, in liters, of the container...Ch. 62 - A seamless brass tube and brass flange assembly is...Ch. 62 - Find the number of cubic centimeters of material...Ch. 62 - Find the weight of the cast-iron angle iron shown....Ch. 62 - Prob. 26ACh. 62 - Prob. 27ACh. 62 - Compute the number of cubic centimeters of...
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- Refer to page 311 for a sequence of functions defined on a given interval. Instructions: • Analyze whether the sequence converges pointwise and/or uniformly on the given interval. • Discuss the implications of uniform convergence for integration and differentiation of the sequence. • Provide counterexamples if any condition fails. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qo Hazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 310 for a matrix and its associated system of differential equations. Instructions: • Find the eigenvalues of the given matrix and classify the stability of the system (e.g., stable, • unstable, saddle point). Discuss the geometric interpretation of eigenvalues in the context of system behavior. • Provide conditions under which the system exhibits periodic solutions. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 313 for a nonlinear differential equation and its linear approximation. Instructions: • Linearize the given nonlinear system around the equilibrium points. • Analyze the stability of each equilibrium using the Jacobian matrix and its eigenvalues. • Discuss the limitations of linearization for determining global behavior. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forward
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