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Given the pair of nonlinear simultaneous equations:
(a) Use the Excel Solver to determine the two pairs of values of x and y that satisfy these equations.
(b) Using a range of initial guesses
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Chapter 11 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- Use Lecture 3 to show that function u defined by u(x,t)= e" sin x is the unique solution of 1 du at n ôx? u(x,0) = 0,u(1,1) = 0, t > 0, u(x,0) = sin x,0arrow_forwardSolve for x and y in terms of z of the given system below. 2х + 5y- 5х— Зу + -2z %3D4 6z = 5arrow_forwardFind a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x is unique. Let 1 3 6 15 4 15 27 69 0 1 1 -4 - 13 - 25 A= b= x= 3 - 63 Find a single vector x whose image under T is b. s the vector x found in the previous step unique? O A. Yes, because there are no free variables in the system of equations. O B. Yes, because there is a free variable in the system of equations. O C. No, because there are no free variables in the system of equations. O D. No, because there is a free variable in the system of equations.arrow_forward3. An oscillator is subject to an external driving force F(t), which is an exponentially decreasing function of time t: F(t) = {Foe-at Find the position of the oscillator at any time t. t20 t<0arrow_forwardSolve for the general solution and type of auxiliary equation of (2D3 – D² + 36D – 18)y= 0 c,ež* + c,cos3v3x+ czsin3v3x; c,ei + €zcos3vZx+ €3$in3v2x; distinct real roots distinct imaginary roots OB. c,e* + c2cos3v4x + C3sin3v4x; repeated imaginary roots c,e* + ¢zcos3v5x+ C3sin3/5x; repeated real roots Oc. OD.arrow_forwardA. Find the values of a such that vectors and are orthogonal. B. Find the domains of the vector-valued function 7(t) = e' i+ j+ In(t? – 4) karrow_forward2. Find the function o(x, y, =) such that Vo=[2xy'+ yz]i +[3x y +xzli+[5z*+xy]k 3. An ant is traveling along the edge of a helix-shaped surface and the path. byarrow_forwardThe power series representation of the function centered at the origin is shown below. Find c - b - a. 5-x = Σx¹ [a(br) - b(c)"] 2x² + x1 n=0arrow_forwardFind the general solution for the following differential equation (r +3). fip + (x+ 4)y = x²e- = r*e drarrow_forwardThe differentials of point functions are exact differentials. Select one: O True Falsearrow_forwardA linear system satisfies the properties of superposition and homogeneity. O True Falsearrow_forwardFind the solution by using the simplex method? MAX Z= 2X1+3X2+X3 S. T: 3X1+6X2+X3 ≤ 6 4X1+2X2+X3 ≤ 4 X1-X2+X3 ≤ 3 X1, X2,X3 20arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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