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1. Given: p: x > 4; q: x <= -2. Translate the following into Boolean Expressions...
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean algebra (show...
Simplify the following Boolean expressions to the minimum number of terms using the properties of Boolean algebra (show your work and write the property you are applying). State if they cannot be simplified A. X’Y + XY B. (X + Y)(X + Y’) C. (A’ + B’) (A + B)’ D. ABC + A’B + A’BC’ E. XY + X(WZ + WZ’)
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions...
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions for the following quantities in where p 0,0 < 0 < 2t. If n is an terms of p, ф, z and p, ф, 2. (а) Vф; (b) Vр"3; (c) V2(p2 cos ); (d) V :(pp + pфф + z2); (F) V. (p*-1 sin(nф)р + pr-1 cos(nф)ф). (e) V x
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by...
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy...
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14)...
1. (9 points, 3 points each) Using the Boolean identities, simplify the following expressions: a. (x7)Zi)(2+...
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)
Marginal costs of production are given by the following function: MC(Q) = 4 − Q Q ≤ 2 ,2Q − 2 Q > 2 (a) Plot the marg...
Marginal costs of production are given by the following function: MC(Q) = 4 − Q Q ≤ 2 ,2Q − 2 Q > 2 (a) Plot the marginal cost curve. (b) Give the expressions for V C(Q) and AV C(Q). (c) Plot AV C(Q) on the plot from (a). (d) Give the expression for the supply curve of this firm. (e) Is it possible to find a different MC(Q) function that gives rise to the same supply curve? If yes,...
2. Let p(x), q(x) denote the following open statements: p(x) 9(г) : x 1 is odd...
2. Let p(x), q(x) denote the following open statements: p(x) 9(г) : x 1 is odd x< 3 If the universe consists of all integers, circle which of the following are TRUE and cr oss out the ones that are FALSE: q(1) p(7) V q(7) P(3) -(p(-4) V q3)) P(3) A q(4) 3ax [p(r) A q(x) p4) A3) (г)Ь ТА
2. Let p(x), q(x) denote the following open statements: p(x) 9(г) : x 1 is odd x
2. Let X~Bin(n, p) with n known. State whether the following expressions are statistics or not....
2. Let X~Bin(n, p) with n known. State whether the following expressions are statistics or not. If an expression is not a statistic, explain why. (a) The number of successes X observed in n trials The sample proportion of successes D (c) z -, where X ~ N(5,4) p-P (d)-p I-D
B. Let p and q be distinct positive prime numbers. Set a p+ (a) Find a...
B. Let p and q be distinct positive prime numbers. Set a p+ (a) Find a monic polynomial f(x) EQlr of degree 4 such that f(a) 0. (b) Explain why part (a) shows that (Q(a):QS4 (c) Note: In order to be sure that IQ(α) : Q-4, we would need to know that f is irreducible. (Do not attempt it, though). Is it enough to show that f(x) has no rational roots? (d) Show V pg E Q(α). Does it follow...
The market demand and market supply of wooden chairs are given below: Q 30 2P Q...
The market demand and market supply of wooden chairs are given below: Q 30 2P Q 103P (1) (2) (a) Identify which one is the demand equation and why? (b) Identify which one is the supply equation and why? (c) What is the equilibrium price (P) and equilibrium quantity (Q)? (d) Describe the market situation if market price (P) is 6 (e) Describe the market situation if market price (P) is 10
10. Let p(x) +1. Let E be the splitting field for p(x) over Q. a. Find the resolvent cubic R(z). ...
Part D,E,F,G
10. Let p(x) +1. Let E be the splitting field for p(x) over Q. a. Find the resolvent cubic R(z). b. Prove that R(x) is irreducible over Q. c. Prove that (E:Q) 12 or 24. d. Prove: Gal(E/Q) A4 or S4 e. If p(x) (2+ az+ b)(a2 + cr + d), verify the calculations on page 100 which show that a2 is a root of the cubic polynomial r(x)3-4. 1. f. Prove: r(x) -4z 1 is irreducible in...
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions for the following quantities in where p 0,0 < 0 < 2t. If n is an terms of p, ф, z and p, ф, 2. (а) Vф; (b) Vр"3; (c) V2(p2 cos ); (d) V :(pp + pфф + z2); (F) V. (p*-1 sin(nф)р + pr-1 cos(nф)ф). (e) V x
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by...
Find the complement of the following expressions b) (AB+C)0%E 2. Given the Boolean function F -xy + x'y' y'z 1. Implement it with AND, OR, and inverter 2. Implement it with OR and inverter gates, and 3. Implement it with AND and inverter gate 3. Express the following function in sum of minterms and product of maxterms: a) F(A,B,C,D) - B'DA'D BD b) F (AB+C)(B+C'D) 4.Express the complement of the following function in sum of minterms a) F (A,B,C,D)-2 (0,2,6,11,13,14)...
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)
2. Let p(x), q(x) denote the following open statements: p(x) 9(г) : x 1 is odd x< 3 If the universe consists of all integers, circle which of the following are TRUE and cr oss out the ones that are FALSE: q(1) p(7) V q(7) P(3) -(p(-4) V q3)) P(3) A q(4) 3ax [p(r) A q(x) p4) A3) (г)Ь ТА
2. Let p(x), q(x) denote the following open statements: p(x) 9(г) : x 1 is odd x
2. Let X~Bin(n, p) with n known. State whether the following expressions are statistics or not. If an expression is not a statistic, explain why. (a) The number of successes X observed in n trials The sample proportion of successes D (c) z -, where X ~ N(5,4) p-P (d)-p I-D
B. Let p and q be distinct positive prime numbers. Set a p+ (a) Find a monic polynomial f(x) EQlr of degree 4 such that f(a) 0. (b) Explain why part (a) shows that (Q(a):QS4 (c) Note: In order to be sure that IQ(α) : Q-4, we would need to know that f is irreducible. (Do not attempt it, though). Is it enough to show that f(x) has no rational roots? (d) Show V pg E Q(α). Does it follow...
The market demand and market supply of wooden chairs are given below: Q 30 2P Q 103P (1) (2) (a) Identify which one is the demand equation and why? (b) Identify which one is the supply equation and why? (c) What is the equilibrium price (P) and equilibrium quantity (Q)? (d) Describe the market situation if market price (P) is 6 (e) Describe the market situation if market price (P) is 10
Part D,E,F,G
10. Let p(x) +1. Let E be the splitting field for p(x) over Q. a. Find the resolvent cubic R(z). b. Prove that R(x) is irreducible over Q. c. Prove that (E:Q) 12 or 24. d. Prove: Gal(E/Q) A4 or S4 e. If p(x) (2+ az+ b)(a2 + cr + d), verify the calculations on page 100 which show that a2 is a root of the cubic polynomial r(x)3-4. 1. f. Prove: r(x) -4z 1 is irreducible in...
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