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4) Expand the following expressions (a) loga ſa-l 9 (6) logz + 4 JY 23
Determine which of the following expressions is equivalent to log3 (27) 27x" ys OA 3 +41093* - 5logy OB. 3+ logz(x - 4) - logz(y-5) OC 3(41093* - 5log3v) OD. 3x'y-5 O E 9+ log3(12x) – log3(15)
Need explanation and answer please 1. Using the index notation, expand the following expressions or evaluate the expressions in 3- dimensional space. a) ti Ơijnj d) p ox at 2
Q3: Expand the following functions by partial fraction expansion. Do not evaluate coefficients or invert expressions. 2 (a) x(s) = (5 + 1)(²+1) (s +3) (6) X() – F76+ 16 + 24 g Dos (b) x(s) = 31 sºls + 1) (s + 2)(s + 3) (c) X(s) = 1 (s + 1)(s + 2)(8 + 3)(s + 4)
QUESTION 23 A 3.65 L of H2 gas at 1.25 atm is allowed to expand to a final pressure of 0.85 atm. What is the final volume? A. 5.4L B. 4.4L c. 6.4L D.7.4L
ONLY NEED E THROUGH J 6. Simplify the following expressions: (a) Vas/a3 (b) a2b3/a b (d) (17hyble 6x0.2 = 5y04 (solve for y in terms of x) (f) x=(2-1/2)-1/2 (solve for x) (g)yx (What is log y?) (h) log, (b') (i) b-log,(/x) (j) log,Ib(loga a2
6. Implement the following Boolean expressions using logic gates:o i. L (AB+ AB) (A + B) ii. L ABC + ABC + ABČ rontiers of iii. L = (A+ B). BC iv. L (A+ C). (B D)
11. Evaluate each of the following expressions: a. 4*3/6-4+ Math.pow(7,2) b. (3+4)*7-3 c. 9*2/4+5%3+3 d. 55 55
3" (25%) Give regular expressions for the following languages on {a, b). (a) L,-(a"b": n 4, m 3) (b) The complement of Li. (c) L- (w: w mod 3 03. Note: lw: the length of w (d) L3 w: |w mod 30 naww) appear) 3" (25%) Give regular expressions for the following languages on {a, b). (a) L,-(a"b": n 4, m 3) (b) The complement of Li. (c) L- (w: w mod 3 03. Note: lw: the length of w...
9. Given the following data, determine the nu- merical value of each of the expressions below. Person (i) X 9 8l 5 25 4 6 3le 3 4 d. EY c.ΣΧ, i 3 i-1
A. L=3; K=6 B. L=10; K=6 C. L=7; K=9 D. L=8; K=7 The graph below shows a firm's isoquants and isocosts. The firm is initially producing Q=20 with the cost minimizing combination of K and L, where Q is output, Kis capital and L is labor. Suppose the owner decides to expand production to Q=40. However, he signed a lease on the capital necessary to produce Q=20, which he cannot get out of in the short run. In order to...