Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 43, Problem 12A
Express each ofthe word problems in Exercises 7 through 19 as equations. Let the unknown number equal x and by logical reasoning solve for the value of the unknown. Check the equation by comparing it to the word problem. Does the equation state mathematically what the problem states in words? Check whether the equation is balanced by substituting the value of the unknown in the equation.
A number plus twice the number equals 36. Find the number.
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>tt 1:32
> trend.1m 1m (sales
> summary(trend.1m)
-
tt) #3###23 (i) ####
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2107.220
57.997 36.332e-16 ***
tt
-43.500
3.067 -14.18 7.72e-15 ***
> trend = ts (fitted (trend.1m), start-start (sales), freq-frequency (sales))
sales trend ###23%23 (ii) ####
as.numeric((1:32 %% 4)
> X
> q1
> q2
> q3
> 94
=
=
=
=
-
as.numeric((1:32 %% 4)
as.numeric((1:32 %% 4)
as.numeric((1:32 %% 4)
== 1)
2)
==
== 3)
==
0)
> season.lm = 1m (resid (trend.1m) 0+q1 + q2 + q3 + q4) #3##23%23 (iii) ####
> summary(season.1m)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
q1
-38.41
43.27 -0.888 0.38232
92
18.80
43.27
0.435 0.66719
q3
-134.78
43.27
-3.115 0.00422 **
94
154.38
43.27 3.568
0.00132 **
> season = ts (fitted (season.lm), start=start (sales), freq=frequency (sales))
> Y X season %23%23%23%23 (iv) ####
>ar (Y, aic=FALSE, order.max=1) #23%23%23%23 (v) ####
Coefficients:
1
0.5704
Order selected 1 sigma 2 estimated as 9431
> ar(Y, aic=FALSE,…
Refer to page 52 for solving the heat equation using separation of variables.
Instructions:
•
•
•
Write the heat equation in its standard form and apply boundary and initial conditions.
Use the method of separation of variables to derive the solution.
Clearly show the derivation of eigenfunctions and coefficients. Provide a detailed solution, step-
by-step.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]
Refer to page 20 for orthogonalizing a set of vectors using the Gram-Schmidt process.
Instructions:
• Apply the Gram-Schmidt procedure to the given set of vectors, showing all projections and
subtractions step-by-step.
• Normalize the resulting orthogonal vectors if required.
• Verify orthogonality by computing dot products between the vectors.
Link:
[https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]
Chapter 43 Solutions
Mathematics For Machine Technology
Ch. 43 - Prob. 1ACh. 43 - Prob. 2ACh. 43 - Prob. 3ACh. 43 - Prob. 4ACh. 43 - Prob. 5ACh. 43 - Prob. 6ACh. 43 - Prob. 7ACh. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Express each ofthe word problems in Exercises 7...
Ch. 43 - Prob. 11ACh. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Prob. 13ACh. 43 - Prob. 14ACh. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Express each ofthe word problems in Exercises 7...Ch. 43 - Prob. 17ACh. 43 - Five holes are drilled in a steel plate on a bolt...Ch. 43 - The total amount of stock milled off an aluminum...Ch. 43 - Prob. 20ACh. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - Prob. 24ACh. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - In each of the following problems, refer to the...Ch. 43 - Prob. 29ACh. 43 - Prob. 30ACh. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Prob. 33ACh. 43 - Prob. 34ACh. 43 - Solve for the unknown values in the following...Ch. 43 - Prob. 36ACh. 43 - Prob. 37ACh. 43 - Prob. 38ACh. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Solve for the unknown values in the following...Ch. 43 - Prob. 45ACh. 43 - Prob. 46A
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- Refer to page 54 for solving the wave equation. Instructions: • Apply d'Alembert's solution method or separation of variables as appropriate. • Clearly show the derivation of the general solution. • Incorporate initial and boundary conditions to obtain a specific solution. Justify all transformations and integrations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440AZF/view?usp=sharing]arrow_forwardRefer to page 14 for calculating eigenvalues and eigenvectors of a matrix. Instructions: • Compute the characteristic polynomial by finding the determinant of A - XI. • Solve for eigenvalues and substitute them into (A - I) x = 0 to find the eigenvectors. • Normalize the eigenvectors if required and verify your results. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardExilet x = {a,b.c}dex.x―R> d(a,b) = d(b, c)=1' d(a, c) = 2 d(xx)=0VXEX is (x.d) m.s or not? 3.4 let x= d ((x,y), (3arrow_forward
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