y-axis (0,5) (5,5) *-аxis (0,0) (5,0) (10,0)
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- Two infinite sheets of current flow parallel to the y-z plane as shown. The sheets are equally spaced from the origin by x = 6.1 cm. Each sheet consists of an infinite array of wires with a density n = 15 wires/cm. Each wire in the left sheet carries a current l₁ = 3.3 A in the negative z- direction. Each wire in the right sheet carries a current 1₂ = 4 A in the positive z-direction. R 1₁ H P % % OOOO OOO S X30. Suppose ,m) is a common eigenvector of î² and î₂ . Then î²|l,m) = Î₂|l,m) = Î ± |l,m) = = (1,m|L²|1',m) (1,m|L₂|I',m') (1,m|L₂|1',m') = =SECTION 4-3 DeMorgan's Theorems 9. Apply DeMorgan's theorems to each expression: (a) A + B (e) A(B + C) (f) AB + CD (g) AB + CD (b) AB (c) A + B + C (d) ABC (h) (A + B)C + D) 10. Apply DeMorgan's theorems to each expression: (a) AB(C + D) (b) AB(CD + EF) (c) (A + B+C + D) + ABCD (d) (A + B+ C + D)(AB CD) (e) AB(CD + EF)(AB + CD) 11. Apply DeMorgan's theorems to the following: (a) (ABC)(EFG) + (HIJ)(KLM) (b) (A + BC + CD) + BC (c) (A + B)(C + D)(E + F)(G + H) SECTION 4-4 Boolean Analysis of Logic Circuits 12. Write the Boolcan expression for cach of the logic gates in Figure 4-55. FIGURE 4-55 D B. (a) (b) (c) (d)
- HELP!(3) The natural independent variables for U are (S, V), from dU = TdS – pdV. U = U(S,V) (), instead. Show that U = U (V,T) leads to a much more complicated expression for p, namely gives simple expressions for T and p as T = and ().: Suppose you use (V,T) p = - V dT + f(V), %D T where f (V) is an unknown function of V.This problem is designed to give you practice using the Dirac delta function. Eval- uate the following integrals. Show your reasoning.