Question 2. Determine whether these statements are true or false. (a) 1+1=2 if and only if 2+3=4. (b) 1+1=3 if and only if monkeys can fly. (c) If monkeys can fly, then1+1=3. (d) If 1+1=3, then 2+2=4. 3. Construct a truth table for each of these compound propositions. (a) (pVq) A-s. (b) (p +9) ^ ( p + q). 4. Show that (p +9)^(p+r) and p + (qar) are logically equivalent.

Find the local maximum and minimum values and saddle point(s) ofthe function. If you have three-dimensional graphing software,graph the function with a domain and viewpoint that reveal all theimportant aspects of the function. (Enter your answers as acomma-separated list. If an answer does not exist, enter DNE.) f(x,y) = x^3 + y^3 − 3x^2 − 3y^2 − 9x

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. 181. y = 5 - 3x from y = 0 to y = 4 – 4

C. Which of the following organisms are most closely related? Are any two the same species? On what did you base your answer? 2.0 A B D C Rod Rod Coccus Rod + + Fermentative Oxidative Fermentative Fermentative Characteristics Morphology Gram Reaction Glucose utilization Cytochrome oxidase GC moles % Present Present Absent Absent 48-52 23-40 50-54 49-53

For this week's discussion, you are asked to generate a continuous and differentiable function f (2) with the following properties: • f(x) is decreasing at x = -6 • f(x) has a local minimum at x = -3 • f (x) has a local maximum at x = 3 Hints: • Use calculus! • Before specifying a function f (2), first determine requirements for its derivative f' (2). For example, one of the requirements is that f' (-3) = 0. • If you want to find a function g(x) such that g(-9) = 0 and g(8) = 0, then you could try g(x) = (x + 9) (x – 8). • If you have a possible function for f' (2), then use the techniques in Indefinite Integrals this Module to try a possible f (x). You can generate a plot of your function by clicking the plotting option (the page option with a "P" next to your function input). You may want to do this before clicking "How Did I Do?". Notice that the label "f(2) =" is already provided for you. Once you are ready to check your function, click "How Did I Do?" below (unlimited attempts). Please note that the bounds on the x-axis go from -6 to 6. f(x) = How Did I Do? Try Another

CLEARLY PLEASE Toluene is produced by hydroforming conversion of n-heptane in a Cr203@-A1203 catalyst medium. The operating conditions of the process are given on the flow chart. The solvent used in the process is recovered. CH3CH2CH2CH2CH2CH2CH2 - CH3CH3 + 4H2 Toluene production efficiency is 15% based on n-heptane fed into the process. The solvent ratio used in the extractor is 10 kg solvent / 1 kg toluene. According to this, a. Calculate how much heat must be added or removed to keep the reactor isothermal at 425 °C. b. What is the temperature of the n-heptane or solvent stream leaving the extractor. (The temperatures of the n- heptane and solvent streams can be considered the same.) но | 425 °C Cooler n-Heptane Superheater 425 °C 18°C 18 °C Catalytic Reactor HO Saturated Toluene vapour n-Heptane . 38c Solvent Heat Heat Extractor Still Exchanger Separator 18 °C 120 °C Solvent Solvent+Toluene

Chapter 4: Project Management (CPM & PERT TECHNIQUES) QUESTION 1 A network consists of the following list. Times are given in weeks. Preceding Activity A B C D E F G H I J K Duration 9 2 12 5 6 A A A B B CF ဝ ထt D H GI E, ] 3 2 8 6 2 a. Draw the network diagram. b. Which activities form the critical path? c. What is the duration of the project completion? QUESTION 2 A PERT problem is detailed in the table below. Times are given in weeks. Preceding Activity A B с D E F G H I J K A A A B B CF D H GI E,J Optimistic Time 7 2 8 3 4 6 2 2 6 4 2 Probable Time/ Most likely time 9 2 12 5 6 8 3 2 8 6 2 Pessimistic Time 14 8 16 10 8 10 4 8 16 14 5 a. Calculate the expected time and ES, EF, LF, and LS of each activity. b. Draw diagram network for this project. c. What are the project variance and the project standard deviation? d. What is the estimated completion time? e. What is the probability of completion of the project after week 40?