Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 76, Problem 8A
To determine
(a)
The value of angle
To determine
(b)
The value of angle
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Vector field F is given by
F(r)
=
(x+2, 0, z+2)
and surface A is the locus of points satisfying z + x² + y² = 3 + 2√x² + y² for z > 0.
(Note that the positive square root appears in this expression.)
(a) Sketch by hand (not assisted by any software) surface A.
(b) Evaluate directly (using cylindrical coordinates or otherwise) the surface integral
I =
SS
A
F.ds
where the flux is evaluated in the direction with positive z component.
(c) Evaluate directly the volume-integral
J =
SSS
W
(☑
F) dV
where W is the solid region lying between surface A and the (x, y)-plane.
(d) Hence, without further integration, determine the value of
K =
SS
B
F.dS,
where B is the disc of radius 3 in the (x, y)-plane, centred on the origin, with normal ds
in the positive z direction and justify your answer.
In Problems 1 through 26, find the (real) eigenvalues and associated eigenvectors of the given matrix A. Find a basis for each eigenspace of dimension 2 or larger.
Please provide a clear and detailed solution
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- Please solve Advanced mathematics assignment given on page 10 inside this drive, all the required books, lecture notes and material is given in the drive that I can not upload here so please visit the link and request for the access and solve, do not give inappropriate answer as given in right, I will report. https://drive.google.com/file/d/1RQ2OZK- LSxpRyejKEMg1t2ql5dbpVLCS/view?usp=sharing Solve problem 5 Reported: The text in the image says! Solve this advanced math assignment 2 given in drive link, if there is any problem in link then ple comment, do not waste my question. Linvalid URL removed] The text instructs you to solve an advanced ma assignment 2 that is located in the provided Go Drive link. It also asks you to comment if there any issue with the link instead of wasting the question.arrow_forwardUse laplace transform to find the solution of the initial value problem. C D Earrow_forwardExercise 6.5.1. Consider the function 9 defined by the power series o diw 28x3 g(x) = =x- +3 2 - x4 x5 + 4 5 (a) Is g defined on (-1,1)? Is it continuous on this set? Is g defined on (-1, 1]? Is it continuous on this set? What happens on [-1,1]? Can the power series for g(x) possibly converge for any other points |x| > 1? Explain. (b) For what values of x is g'(x) defined? Find a formula for g'.arrow_forward
- 6. Use Laplace transform to find the solution of the initial value problem. (a) y" +4y' + 4y = 0; (b) y(4)-4y=0; y(0) = 0, y(0) = 1, y'(0) = 1 y'(0) = 1, y"(0) = 0, y" (0) = 2 1arrow_forwardFind An of the cosine series. Could you see if my working is correct? I've attached it with the questionarrow_forwardQ5 Using Hermite's algorithm find s, t = Z so that s² + t² = 101.arrow_forward
- Q4. Find all solutions of 91x² + y² = 1 with x, y Є Z.arrow_forwardQ3. Find all solutions of x² - 29y² = ±1 with x, y ɛ Z.arrow_forwardProblem 11 (Gram-Schmidt). Try the Gram-Schmidt procedure for the vectors, 1 0 2 with respect to the standard dot product on R4. What happens? Can you explain why you are unable to complete the algorithm? Problem 12 (Orthogonal Matrices Preserve Orthogonality). Suppose x, y = Rn" are orthogonal to each other with respect to some inner product (.,.) and that A is an orthogonal matrix and B is some invertible matrix. 1. Prove that Ax and Ay are also orthogonal to each other and that ||x|| = ||Ax|| and ||y|| : = ||Ay||. 2. Is it true that Bx and By are also orthogonal to each other and that ||x|| = ||Bx|| and ||y|| = = ||By||? Provide a proof or a counter-example. Problem 13 (Orthogonal Complement). Let W be the subspace of R5 spanned by, 1 2 2 4 u = 3 , v= 7 2 2 Find a basis of the orthogonal complement W- of W. Verify in this particular example that WW₁ = {0} and that dim(W) + dim(W¹) = 5.arrow_forward
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01 - Angles and Angle Measure in Degrees - Part 1 - Types of Angles & What is an Angle?; Author: Math and Science;https://www.youtube.com/watch?v=hy95VyPet-M;License: Standard YouTube License, CC-BY