Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134668574
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Chapter DPT, Problem 39E
In Problems 39–42, write in the form axp + byq where a, b, p, and q are rational numbers.
39.
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Matrix MЄ R4×4, as specified below, is an orthogonal matrix - thus, it fulfills MTM = I.
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We know also that all the six unknowns mr,c are non-negative with the exception of
Your first task is to find the values of all the six unknowns. Think first, which of the mr,c you should find first.
Next, consider a vector v = (-6, 0, 0, 8) T. What's the length of v, i.e., |v|?
Using M as transformation matrix, map v onto w by w = Mv provide w with its numeric values.
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Finally, consider another vector p = ( 0, 0, 8, 6) T. What's the angle between v (from above) and p?
Using M as transformation matrix, map p onto q by q = Mp - provide q with its numeric values.
What's the angle between w and q, especially when comparing it to the angle between v and p?
(c) Find the harmonic function on the annular region Q = {1 < r < 2} satisfying the
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U (1, 0) = 1,
U(2, 0) 1+15 sin (20).
=
Chapter DPT Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...
Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Give an example of an integer that is not a...Ch. DPT - Prob. 17ECh. DPT - Prob. 18ECh. DPT - Prob. 19ECh. DPT - Prob. 20ECh. DPT - Prob. 21ECh. DPT - In Problems 1724, simplify and write answers using...Ch. DPT - Prob. 23ECh. DPT - Prob. 24ECh. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - Prob. 28ECh. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - Each statement illustrates the use of one of the...Ch. DPT - Round to the nearest integer: (A)173 (B)519Ch. DPT - Multiplying a number x by 4 gives the same result...Ch. DPT - Find the slope of the line that contains the...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - In Problems 37 and 38, factor completely....Ch. DPT - In Problems 37 and 38, factor completely....Ch. DPT - In Problems 3942, write in the form axp + byq...Ch. DPT - Prob. 40ECh. DPT - Prob. 41ECh. DPT - In Problems 3942, write in the form axp + byq...Ch. DPT - Prob. 43ECh. DPT - Prob. 44ECh. DPT - In Problems 4550, solve for x. 45.x2=5xCh. DPT - In Problems 4550, solve for x. 46.3x221=0Ch. DPT - In Problems 4550, solve for x. 47.x2x20=0Ch. DPT - In Problems 4550, solve for x. 48.6x2+7x1=0Ch. DPT - In Problems 4550, solve for x. 49.x2+2x1=0Ch. DPT - In Problems 4550, solve for x. 50.x46x2+5=0
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- 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]arrow_forwardNo chatgpt pls will upvote Already got wrong chatgpt answer Plz .arrow_forward7. (a) (i) Express y=-x²-7x-15 in the form y = −(x+p)²+q. (ii) Hence, sketch the graph of y=-x²-7x-15. (b) (i) Express y = x² - 3x + 4 in the form y = (x − p)²+q. (ii) Hence, sketch the graph of y = x² - 3x + 4. 28 CHAPTER 1arrow_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_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
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- Question 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_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
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