Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Textbook Question
Chapter 63, Problem 32AR
A circular plate with a 15.00-inch radius is cut from a rectangular aluminum piece that is 3'0.0". wide and 4'0.0" long. Before the circular plate was cut, the rectangular piece weighed 30.00 pounds. Find the weight of the circular plate. Round the answer to the nearest tenth pound.
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No chatgpt pls will upvote Already got wrong chatgpt answer
(c) Find the harmonic function on the annular region Q = {1 < r < 2} satisfying the
boundary conditions given by
U (1, 0) = 1,
U(2, 0) 1+15 sin (20).
=
Question 3
(a) Find the principal part of the PDE AU + UÃ + U₁ + x + y = 0 and determine
whether it's hyperbolic, elliptic or parabolic.
(b) Prove that if U(r, 0) solves the Laplace equation in R², then so is
V(r, 0) = U (², −0).
(c) Find the harmonic function on the annular region = {1 < r < 2} satisfying the
boundary conditions given by
U(1, 0) = 1,
U(2, 0) = 1 + 15 sin(20).
[5]
[7]
[8]
Chapter 63 Solutions
Mathematics for Machine Technology
Ch. 63 - Prob. 1ARCh. 63 - Express each area in Exercises 1 through 6 as...Ch. 63 - Express each area in Exercises 1 through 6 as...Ch. 63 - Express each area in Exercises 1 through 6 as...Ch. 63 - Prob. 5ARCh. 63 - Express each area in Exercises 1 through 6 as...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...
Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The following Exercises 7 through 19 involve...Ch. 63 - The cross section of a dovetail slide is shown....Ch. 63 - Compute the area of the pattern shown. Round the...Ch. 63 - The following Exercises 22 through 27 involve...Ch. 63 - The following Exercises 22 through 27 involve...Ch. 63 - The following Exercises 22 through 27 involve...Ch. 63 - The following Exercises 22 through 27 involve...Ch. 63 - The following Exercises 22 through 27 involve...Ch. 63 - The following Exercises 22 through 27 involve...Ch. 63 - Find the area of each of the segments ACB for...Ch. 63 - Prob. 29ARCh. 63 - Find the area of each of the segments ACB for...Ch. 63 - Find the area of the shaded segment shown. Round...Ch. 63 - A circular plate with a 15.00-inch radius is cut...Ch. 63 - Compute the cross-sectional area of the grooved...Ch. 63 - Find the area of the pattern shown. Round the...Ch. 63 - Prob. 35ARCh. 63 - Express each volume in Exercises 35 through 40 as...Ch. 63 - Prob. 37ARCh. 63 - Express each volume in Exercises 35 through 40 as...Ch. 63 - Express each volume in Exercises 35 through 40 as...Ch. 63 - Express each volume in Exercises 35 through 40 as...Ch. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Prob. 45ARCh. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Prob. 47ARCh. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Prob. 49ARCh. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Prob. 51ARCh. 63 - Prob. 52ARCh. 63 - Prob. 53ARCh. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Prob. 56ARCh. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Solve these prism and cylinder exercises. Where...Ch. 63 - Prob. 60ARCh. 63 - Prob. 61ARCh. 63 - Diameter 9.050 centimeters; Volume Round the...Ch. 63 - Prob. 63ARCh. 63 - Volume = 42.98 cubic inches; Diameter = Round the...Ch. 63 - Volume = 775 cubic centimeters; Diameter = Round...Ch. 63 - The side view of a steel roundhead (hemisphere)...Ch. 63 - Prob. 67ARCh. 63 - A hollow glass sphere has an outside circumference...Ch. 63 - Prob. 69ARCh. 63 - Compute the number of cubic centimeters of iron...
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- No chatgpt pls will upvote Already got wrong chatgpt answer Plz .arrow_forward- (c) Suppose V is a solution to the PDE V₁ – V× = 0 and W is a solution to the PDE W₁+2Wx = 0. (i) Prove that both V and W are solutions to the following 2nd order PDE Utt Utx2Uxx = 0. (ii) Find the general solutions to the 2nd order PDE (1) from part c(i). (1)arrow_forwardSolve the following inhomogeneous wave equation with initial data. Utt-Uxx = 2, x = R U(x, 0) = 0 Ut(x, 0): = COS Xarrow_forward
- Could you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.arrow_forward(a) Write down the general solutions for the wave equation Utt - Uxx = 0. (b) Solve the following Goursat problem Utt-Uxx = 0, x = R Ux-t=0 = 4x2 Ux+t=0 = 0 (c) Describe the domain of influence and domain of dependence for wave equations. (d) Solve the following inhomogeneous wave equation with initial data. Utt - Uxx = 2, x ЄR U(x, 0) = 0 Ut(x, 0) = COS Xarrow_forwardQuestion 3 (a) Find the principal part of the PDE AU + Ux +U₁ + x + y = 0 and determine whether it's hyperbolic, elliptic or parabolic. (b) Prove that if U (r, 0) solves the Laplace equation in R2, then so is V (r, 0) = U (², −0). (c) Find the harmonic function on the annular region 2 = {1 < r < 2} satisfying the boundary conditions given by U(1, 0) = 1, U(2, 0) = 1 + 15 sin(20).arrow_forward
- 1c pleasearrow_forwardQuestion 4 (a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation U₁ = Uxx, x > 0. (b) Consider the solution U(x,t) = (sin x)e¯t of the heat equation U₁ = Uxx. Find the location of its maxima and minima in the rectangle Π {0≤ x ≤ 1, 0 ≤t≤T} 00} (explain your reasonings for every steps). U₁ = Uxxx>0 Ux(0,t) = 0 U(x, 0) = −1arrow_forwardCould you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.arrow_forward
- Could you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.arrow_forward(b) Consider the equation Ux - 2Ut = -3. (i) Find the characteristics of this equation. (ii) Find the general solutions of this equation. (iii) Solve the following initial value problem for this equation Ux - 2U₁ = −3 U(x, 0) = 0.arrow_forwardQuestion 4 (a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation U₁ = Uxx, x > 0. (b) Consider the solution U(x,t) = (sin x)et of the heat equation U₁ = Uxx. Find the location of its maxima and minima in the rectangle πT {0≤ x ≤½,0≤ t≤T} 2' (c) Solve the following heat equation with boundary and initial condition on the half line {x>0} (explain your reasonings for every steps). Ut = Uxx, x > 0 Ux(0,t) = 0 U(x, 0) = = =1 [4] [6] [10]arrow_forward
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