Question The cantilever shown below has a rectangular cross-section and bears a concentrated load F at the free end. If the yield stress is 350 MPa and the safety factor against yielding is nu, calculate the greatest possible value of F. - 2 m Select one: AF...8.2 kN B. F = 32.8 kN 100 mm - Cross-section C. Fra = 16.4 kN D. Fraz = 20.56 kN

Shown in the figure below is a system that executes a power cycle while receiving Q1 = 600 Btu by heat transfer at a temperature of T1 = 1500°R and discharging Q2 = 400 Btu by heat transfer at a temperature of T2 = 800°R. A third heat transfer occurs at a temperature of T3 = 600°R. These are the only heat transfers experienced by the system.(a) Applying an energy balance together with Eq. 5.13, determine the minimum and maximum values for Q3, in Btu, for the heat transfer at T3 = 600°R.(b) For the power cycle, evaluate the maximum theoretical thermal efficiency. ►WeyckcycleT2T3Q2

1.[3 marks] Evaluate: ∫ ∫ ∫E z(x2 + y2 + z2)-3/2 dV where E is the region satisfying the following inequalities: x2 + y2 + z2 ≤ 16, z ≥ 2.

Problems 3.2(e,f), 3.4(e,f), 3.5(b,c), 3.6(c,d), 3.10(a,b), 3.11, 3.12(b), 3.15(a,c) 140 Chapter 3 Gate-Level Minimization Problems 141 3.4 Simplify the following Boolean functions, using K-maps: (a) F(x,y, z) (2,3.6,7) (c)' F(A,B,C,D)=Σ(3,7, ll, 13, 14, 15) (e) F (w, x, y, z) = Σ(11, 12, 13, 14, 15) (g) F(w, x, y, z)=E(0.1.4,5,10,1 1,14,15) Simplify the following Boolean functions, using four-variable K-maps: (a)" F (w, x, y, z) = Σ(1, 4, 5, 6, 12, 14, 15) (b)" F (A, B, C, D) = Σ(2, 3, 6, 7, 12, 13, 14) (c) F (w, x, y, z) = Σ(1, 3, 4, 5, 6, 7, 9, 1 1, 13, 15) (d)' F (A, B, C, D) = Σ (0, 2, 4, 5, 6, 7, 8, 10, 13, i5) Simplify the following Boolean expressions, using four-variable K-maps: (a) A'B'C'D AC'D' B'CDA'BCD BCD (by (d)' (f) (h) F (A, B, C, D) = Σ(4. 6, 7, 15) F(w.rry, z)_E(2.3. I2. 13, 14, 15) F (w, x, y, z)-S(8, 10, 12, 13.4) F(w, x, y, z)-E(2.3.6.7.8.9.12,I3) UDP 02467 3.5 FIGURE 3.40 Schematic for Circuit with UDP_02467 3.6 Although Verilog HDL uses this kind of description for UDPs only, other HDLs and computer-aided design (CAD) systems use other procedures to specify digital circuits in tabular form. The tables can be processed by CAD software to derive an efficient gate structurc of the design. None of Verilog's predefined primitives describes sequential logic. The model of a sequential UDP requires that its output be declared as a reg data type, and that a column be added to the truth table to describe the next state. So the columns are organized as inputs: state: next state. (c) A'B'CD AB'D +A'BC ABCD AB'C (d) A'B'C'D' BC'D A'C'D A'BCD +ACD' Simplify the following Boolean expressions, using four-variable K-maps: 3.7 In this section, we introduced the HDLs and presented simple examples to illustrate alternatives for modeling combinational logic. A more detailed presentation of model- ing with HDLs can be found in the next chapter. The reader familiar with combinational circuits can go directly to Section 4.12 to continue with this subject. (c) AB C B'C'DBCD ACD'+ A'B'C+ A BC D Find the minterms of the following Boolean expressions by first plotting each function in a K-map: 3.8 (a) xy yz + xy'z (b) C'D+ABC ABD' +A'B'D (d) A'B A'CD B'CD BC'D VHDL-Truth Tables 3.9 Find all the prime implicants for the following Boolean functions, and determine which are essential: (a)" F(w, x, y, z) = Σ(0, 2, 4, 5, 6, 7, 8, 10, 13, 15) (b), F (A, B, C, D) = Σ(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) (c) F (A, B, C, D) = Σ(2, 3, 4, 5, 6, 7, 9, 11, 12, 13) (d) F(w,x, y, z)=E(1.3, 6, 7, 8, 9, 12, 13, 14, 15) (e) F (A, B, C, D) = Σ(0, 1, 2, 5, 7, 8, 9, 10, 13, 15) (f) F(w, x, y, z)=E(0.1, 2, 5, 7, 8, 10, 15) Simplify the following Boolean functions by first finding the essential prime implicants: (a) F (w, x, y, z) 2(0, 2, 5, 7, 8, 10, 12, 13, 14, 15) (b) F(A, B,C, D) 2(0,2,3,5,7,8,10, 11, 14, 15) (e)* F(A, B,C,D)-(1,3,4,5, 10, 11, 12, 13, 14, 15) (d) F (w, x, y, z) = Σ(0, 1, 4, 5, 6, 7, 9, 11, 14, 15) (e) F (A, B, C, D)-Σ(0.1, 3, 7, 8, 9, 10, 13, 15) (f) F (w, x, y, z) = Σ(0, 1, 2, 4, 5, 6, 7, 10, 15) VHDL does not support truth tables directly. Instead, a truth table has to be converted into a set of Boolean equations, which can be described by signal assignment statements. PROBLEMS (Answers to problems marked with appear at the end of the text.) 3.10 1 Simplify the following Boolean functions, using three-variable K-maps: (a) F(x, y, z) = Σ (0, 2, 4, 5) (c) Fr, y, )-20,1,2,3, 5) (b) F(x,y, z)-2(0, 2, 4, 5, 6) (d) , y, z)=E(1,2,3,7) 2 Simplify the following Boolean functions, using three-variable K-maps: (b)" F(x, y, z) = Σ(1, 2, 3, 6, 7) (d) F(x, y, z) = Σ( 1, 2, 3, 5, 6, 7) (f) F(x, y, z)=E(3, 4, 5, 6, 7) (a)" F(x, y, z) = Σ (0, 1, 5, 7) (c) Fx,y, z) (2,3,4,5) (e) P(x, y, z) = Σ(0,2,4,6) Simplify the following Boolean expressions, using three-variable K-maps: (a)'. F (x.yz) = xy + x'y'z, + χ,yz (c)" F (x, y, z) = x,y + yz' + y,z' 3.11 Using K-maps for Fand F,convert the following Boolean function from a sum-of-prod- 3.3 ucts form to a simplified product-of-sums form. (d) F(x, y, z) = x,yz + xy,z' + xy'z F(w ryz)0,,2, 5,8, 10, 13)

Please help solving problem 1,2 and 3. Thank you very much. For questions 1 - 3, consider the following test results obtained for a surface water sample. lon Concentration (ppm) Ca2+ 36.0 Mg2+ 10.8 Na 12.4 K 5.9 нсоз" 82.1 SO42 32.0 CI 16.9 NO3 7.4 1. Check the accuracy of the analytical measurements. Do you suspect that a constituent of significance has been neglected? If so, is it a cation or an anion? 2. Determine the mole fraction of calcium, magnesium, and sulfate for the water sample given above. 3. Determine this water's hardness and alkalinity in mg/L as CaCO3.

Die-rolling experiment: 1) Acquire any "fair-enough" die. 2) Roll it at least 100 times (each person for themselves). 3) Note what the outcome is overy time. 4) For each group of 5 (go consecutively, i.e. group first five rolls, then the next five rolls, etc.), take the average of the 5 rolls. For example, if the first five rolls are \( 3,6,1 \), 5 , and 3 , Die-rolling experiment: 1) Acquire any "fair-enough" die. 2) Roll it at least 100 times (each person for themselves). 3) Note what the outcome is overy time. 4) For each group of 5 (go consecutively, i.e. group first five rolls, then the next five rolls, etc.), take the average of the 5 rolls. For example, if the first five rolls are \( 3,6,1 \), 5 , and 3 , the average will be \( 18 / 5=3.6 \). 5) You will end up with at least 20 averages. Plot these averages on a \( 2 \mathrm{D} \) column graph. Alternatively, you can do a histogram of your results, which will be a fancier way of doing a 2D column graph. With a histogram though, you can control the bin size and instead of each individual average (e.g. 3.2, 3.4. 3.6, etc.). you can group them together with a bin size of 1 . Bonus credits will be assigned to those showing their results with a histogram of bin size 1 in addition to their regular \( 2 \mathrm{D} \) column graphs. 6) All the probabilities of \( 1,2,3,4,5 \) and 6 are \( 1 / 6 \) with a fair die. Therefore, the probabilities are said to be "uniformly distributed". Then, why is your \( 2 D \) column graph / histogram not looking uniform at all? Speculate / comment on the rationale for this.

Units V.C represents which quantity? Select one: a. Electric potential energy, U b. Electric Constant, k c. Electric Potential d. Electric Flux, F e. Electric Field, E