Question 2 1 pts The function u = − - x³ y² (−6 x + y − 6) – (2 x − y − z)² has a critical point p = (−1/2, 2, −3). For k = 1, 2, 3, compute the determinant D½ of the upper-left kk submatrix of the Hessian H(p). (See class notes or Theorem 8 in section 10.7 of the text.) Define C = 0 if the Hessian second derivative test fails, C = 2 if µ is a local minimum, C = 4 if it is a local maximum, and C = 8 if it is a saddle. Then the number sin D₁ + sin D2 + sin D3 + sin C is -2.881 O 1.741 -0.139 -2.177 0.407 3.521 -3.055 O 2.773

Plz do all parts if u can..

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det(A?) = 8. 1693619 B det (;A) = 2. u10121 1101210007 1693619210 det(A – B) = -2. u10121 %3D 101 0007- 16 210 det(B") = 210 det(B¯'A") = 01210007 A and B 3x3 matrixes and determinant(A)=4 and determinant(B)=6 . for the options given above whats true? 19210 1012 0121 e Message 12:10 (09:28) II 2/3

1. Show that if the Wronskian of Y₁ and Y₂ is nonzero then so is the Wronskian of 2Y₁ and Y₁ + Y₂. 2. Calculate the determinant of the matrix and simplify det 104 -218 2 3 3 3. Write down a differential equation for which Yp(t) = (At² + Bt) cos(4t) + (Ct² + Dt) sin(4t) could be the guess for the Method of Undetermined Coefficients.

2. [E2.1-Q33(a)] Show that the value of the determinant is independent of 0. sin - cos 0 sin cos sin 0 cos sin 0 + cos 0 0 1

Consider a damped undriven oscillator whose equation of motion is given by * = -w²x-yi Assume that the system is critically damped, such that r = solution is given by r(t) = (A + Bt)ert/2 2wo. When this is the case, a general where A and B are constants. A) Express the general solution as a complex function. [Hint: This is a trick question.] B) Assume the oscillator is initially at rest at the origin. At t = 0, it is given an impulse T (i.e., a sudden blow), causing it to launch with initial positive velocity vo. Determine specific expression for both x(t) and v(t) in terms of known values. C) Determine both the time when the velocity is zero and the time when the velocity starts to increase (i.e., when the acceleration changes sign). D) Extending from parts b and c, sketch both x(t) and v(t), making sure to clearly indicate the relevant values (e.g., the maximum displacement, etc...). [Hint: The velocity is zero when the object is at the maximum displacement.

please solve it on paper

1. Solve for x and y in xy + 8 + j(x²y + y) = 4x + 4 + j(xy² + x) A. 2, 2, B. 2,3 C. 3, 2 2. Determine the principal value of (3 + j4)¹ +² +j2 A. 0.42+j0.56 C. -0.42-j0.66, B. 0.42+j0.66 D. 0.42-j0.66 3. Using the properties of complex numbers. determine the two square roots of 3-j2 A. +1.82+j0.55, C. 1.82 + j0.55 B. +1.82±j0.55 D. +1.82 + j0.55 4. Evaluate: BE CALC 3-14 3+14 + 3+j4 3-j4 A. 2.44 +j4/ B. 2.44-j4 C. -2.44 + j4 D. 2.44 +j5 Evaluate log; (3 + j4). A. 0.6+j1.02 C. -0.6-j1.02 B. -0.6+j1.02 D. 0.6-j1.02, 6. The following three vectors are given; A = 20 +j20, B = 30/120° and C= 10+ j0, find AB/C C. 95/-50° B. 85-75% A. 70/45° D. 75/70" 7. If 100+5x/45° = 200/-e. Find x and 8. A. 24. 23.28 B. 23.28. 32.3° C. 23.28. 24.3% D. 23, 42.8° 8. Determine the principal value of cosh' (j0.5). A. In (1+j5) C. In j5 B. In (1± √5), D. In j(1 + √5) 2 5 1 = 9. In A-2B-C=0. if A= 2B-C-0. if A- and B-₁ find C |² -1 3 2 3 8 -3 8 3 91 C. A. 3 0 0 -3 -8 -8 -3 3 D. B. | 3 0 -3 10. Solve for a and b…