Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 73, Problem 5AR
To determine
The function of the given angle.
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1. [10 points] Given y₁(x) = x²² is a solution to the differential equation x²y"+6xy'+6y=0 (x>0), find a
second linearly independent solution using reduction of order.
>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]
Chapter 73 Solutions
Mathematics For Machine Technology
Ch. 73 - With reference 1, name the sides of each of the...Ch. 73 - With reference to 1, name the sides of each of the...Ch. 73 - Prob. 3ARCh. 73 - Prob. 4ARCh. 73 - Prob. 5ARCh. 73 - Prob. 6ARCh. 73 - Prob. 7ARCh. 73 - Prob. 8ARCh. 73 - Prob. 9ARCh. 73 - Prob. 10AR
Ch. 73 - Prob. 11ARCh. 73 - Prob. 12ARCh. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in degrees and minutes that...Ch. 73 - Determine the values A in decimal degree to 2...Ch. 73 - Determine the values A in decimal degree to 2...Ch. 73 - Determine the values A in decimal degree to 2...Ch. 73 - For each of the following functions of angles,...Ch. 73 - For each of the following functions of angles,...Ch. 73 - For each of the following functions of angles,...Ch. 73 - For each of the following functions of angles,...Ch. 73 - Solve the following exercises. Compute angles to...Ch. 73 - Solve the following exercises. Compute angles to...Ch. 73 - Solve the following exercises. Compute angles to...Ch. 73 - Prob. 29ARCh. 73 - Prob. 30ARCh. 73 - Prob. 31ARCh. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Solve the following applied right triangle...Ch. 73 - Prob. 40ARCh. 73 - Prob. 41ARCh. 73 - Prob. 42ARCh. 73 - Prob. 43ARCh. 73 - Prob. 44ARCh. 73 - Prob. 45ARCh. 73 - Prob. 46ARCh. 73 - Prob. 47ARCh. 73 - Prob. 48ARCh. 73 - Prob. 49ARCh. 73 - Determine the sine, cosine, tangent, cotangent,...Ch. 73 - Determine the sine, cosine, tangent, cotangent,...Ch. 73 - Prob. 52ARCh. 73 - Prob. 53ARCh. 73 - Determine the sine, cosine, tangent, cotangent,...Ch. 73 - Prob. 55ARCh. 73 - Prob. 56AR
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- 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]arrow_forwardRefer 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_forward
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