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1. Let k be an integer. Solve the following: (b) ;-164+3 (c) (754-3)(-+1) 2. Solve each...
1. (9 points, 3 points each) Using the Boolean identities, simplify the following expressions: a. (x7)Zi)(2+ y) b. 7(xyz) + y(ż + (7 +z)) C. (xz + ✓x) + y(x+y)(7+ y)
Ifz-I+),22-1-j, and 3=-2, calculate the magnitude and phase (in radians) of (a) zi (b) z2 (c) z3 (d) z1 +z (e) z z3 (f) z1z2 (g) t22 (h) 을 2. 21 23 21-23 Z1
Solve the following system of algebraic equations. a. ?=?2 and ?=3? b. 2?=?2 and ?=4−?2 c. 12?−?=0 and 3?2−4?−8=0
Solve the following equations: a) log2 (2) + log2 (3x - 5) = 3 b) 22+3 = 7° c) log(+4) + loge(x+3) = 1 d) 4e-2 = 31
1.a. b. c. Solve the IVP 2 [:] = [3 =:] [:] []=[3] ņ Find e At where 2 5 A = -2 -4 Solve the IVP (21-1 -3) M (O)-() x(0) I g(0)
(1) Simplify the following expressions as much as possible. c) (-1+1)2(1)(i(21+1)+δ(-21+1)] (Draw also the resulting function for part (c))
Solve the following quadratic equations: 1) 2x2+ 6x+ 1 = 0 2) 4x2+ 12x+ 2 = 0 3) 9x2−4x+ 12 = 0 4) (x−1)(x+ 3 +3(x−1))=(4−x)(x−1)(x−1) Hint:Factor and simplify using (x−1).
Simplify the following indicial expressions as much as possible. ΣΣ1C,B (a) Substitute Cii = -1 AipBpj into a = k 1 Hint: Consider changing the index j to index k in the expression for C;i 3 ( b) Σ-Σ_ Σ1 Α, Βιδικ - Σ Σ Σ-12AB , im rį=1 i=1 m=1 Hint: Use the index substitution property of Kronecker delta first to simplify the expression. When you do that, the triple summation will reduce to double summation in each symbol...
Solve the following set of three equations for ?1,?2 and ?3. ?3 = ?1 + ?2 −30?1 − 41?3 + 45 = 0 −30?1 + 21?2 − 80 = 0 Comment: "If possible. I'd like to see the steps, please. Thanks"
2. Suppose that you were to try to find a parabola y az2 +bz c that passes through the (x, y) pairs (-4,7), (-1,-3), and (1,6). To obtain the coefficients a, b, and c you would try to solve a system of linear equations whose augmented matrix is which of the following? 16 -4 1 49 16 -4 1 7 (a)9-1-3(b)11 1 9(1-1 1 -3 36 1 1 6 49 7 1 16 (d)1 -3 1-1(e)9 3 1 1 36...