Question 65 – A differential equation is given as y” + 5y’ + 6y = 0, y(0) = 2 and y’(0) = 3. By using Laplace transform, an engineer has correctly produced the equation L {y} = (2s + 13) / [(s + 2)(s + 3)] = A / (s + 2) + B (s + 3). (a) Find the values of A and B. (b) The inversed Laplace transform of 1 / (s + a) is given by exp (-at) where a is a constant. If the statement : L {y} = 9 L { exp (-2t) } - 7 L { exp (-3t) } is correct, find the equation of y as a function of t as a solution to the differential equation stated in the beginning of this question. When L {d} = 9 L {b} - 7 L {c}, then d = 9b - 7c with b, c and d are unknowns.
Answer / kang chuen tat (malaysia - pen
Answer 65 – (a) Let (2s + 13) / [(s + 2)(s + 3)] = [A (s + 3) + B (s + 2)] / [(s + 2)(s + 3)]. Then 2s + 13 = As + 3A + Bs + 2B = (A + B)s + (3A + 2B), then A + B = 2 and 3A + 2B = 13. Let 2A + 2B = 4 as first equation by doubling A + B = 2 and 3A + 2B = 13 as second equation, the difference of first and second equations will produce A = 9. When A = 9, B = 2 - A = 2 - 9 = -7. (b) Let d = y, b = exp (-2t) and c = exp (-3t), then y = 9 exp (-2t) - 7 exp (-3t). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
| Is This Answer Correct ? | 0 Yes | 0 No |
Are there any methods of preventing cracking of carbon steel welds in refining environments?
What is Vacuum? If pressure is less than that of atmospheric, can we call it vacuum? If so some places have less atmospheric pressures, can we call people living there are living in vacuum?
FOOD ENGINEERING - QUESTION 23.1 : (a) According to United States Department of Agriculture (USDA) (http://ndb.nal.usda.gov/ndb/search/list, accessed 12 August 2016), 100 g of potatoes generate 77 kcal of energy. For raw tomatoes, 111 g have 18 kcal of energy. Question : How much energy will one gain if 150 g of heated potatoes are eaten with 200 g of raw tomatoes? (b) If 1 Calorie = 1 food Calorie = 1 kilocalorie and 1000 calories = 1 food Calorie, then how many Calories are there in 9600 calories? (c) According to a food package of potato chips, 210 Calories are produced per serving size of 34 g. In actual experiment of food calorimetry lab, 1.75 g of potato chips, when burnt, will produce 9.6 Calories. For each serving size of potato chip, find the difference of Calories between the actual experimental value and the value stated on the food package. (d) The specific heat of water is c = 1 cal / (g.K) where cal is calorie, g is gram and K is Kelvin. Then what is the temperature rise of water, in degree Celsius, when 150 g of water is heated by 9600 calories of burning food?
Are there any alternatives to scraping a shell and tube if a capacity increase will make the pressure drop across the exchanger too large?
MICROBIOLOGICAL ENGINEERING - QUESTION 28.3 : In the calculation of the growth of bacteria, absorbance, A in spectrophotometry is used. According to Beer-Lambert Law, A = e x l x c where A is the absorbance of the solution (no unit), l is the distance of light travels through the solution (in cm), e is the molar absorptivity or the molar extinction coefficient [ in L / (mol.cm) ]. For a particular solute and fixed path length : As / Ao = Cs / Co where Ao is the observed signal for a known concentration Co, and As is the observed signal for a sample concentration Cs. (a) For a cell concentration of 560 cells / mL, a spectrophotometre gives an absorbance reading of 1.0. A mixture of concentration 3600000 cells / mL can be diluted in several operations, with each operation having a dilution of 1:20. How many dilutions should be made so that the concentration of this mixture can be calculated within a range of A = 0.0 to 1.0. (b) In another experiment, a sample tube of 1 cm in width is used. Let A = 0.06 and e = 0.0012 ml / (cell.cm). Find the cell concentration of the sample.
What's -74C, dew point is better the -70C dew point In draying unit .
What are the three classes of organic solvents?
What is a solvent?
Question 109 - (a) Acceptable wavefunction in quantum mechanics in the range of : negative infinity < x < positive infinity, vanishes at least at one boundary. Which of the following is the wavefunction or are the wavefunctions of acceptable theory : P = x, P = | x |, P = sin x, P = exp (-x), P = exp (-| x |)? State the reason. (b) Let linear momentum operator P = -ih d / dz. The wavefunction is S = exp (-ikz) where i x i = -1, k and h are constants. Find the linear momentum of such wavefunction by using the term P x S.
In a crusher where is the energy provided to it is used up for?
At 150 degree Celsius, a mixture of 40 wt % Sn and 60 wt % Pb present, forming phases of alpha and beta. Chemical composition of Sn at each phase : CO (overall) : 40 %, CA (alpha) : 11 %, CB (beta) : 99 %. (a) State 2 reasons for the existences of alpha and beta phases for the mixture of Sn – Pb at 150 degree Celsius. (b) By using Lever Rule, calculate the weight fraction of each phase for alpha, WA = Q / (P Q) and beta, WB = P / (P Q) where Q = CB – CO and P = CO – CA.
BIOPROCESS ENGINEERING - EXAMPLE 14.2 : An aqueous solution with 2.5 g of a protein dissolved in 600 cubic centimeters of a solution at 20 degree Celsius was placed in a container that has a water-permeable membrane. Water permeated through the membrane until the h - level of the solution was 0.9 cm above the pure water. (a) Calculate the absolute temperature of the solution, T in Kelvin, where T (Kelvin) = T (degree Celsius) + 273.15. (b) Calculate the osmotic pressure, P of the solution by using the formula P = hrg where h is level of the solution, r is density of water with 1000 kg per cubic meter, g = 9.81 N / kg as gravitational acceleration. (c) Calculate the concentration of the protein solution, C in kg / cubic meter. (d) Calculate the molecular weight of the protein, (MW) = CRT / P where R = 8.314 Pa cubic meter / (mol K) as ideal gas constant.
Civil Engineering (5086)
Mechanical Engineering (4456)
Electrical Engineering (16639)
Electronics Communications (3918)
Chemical Engineering (1095)
Aeronautical Engineering (239)
Bio Engineering (96)
Metallurgy (361)
Industrial Engineering (259)
Instrumentation (3014)
Automobile Engineering (332)
Mechatronics Engineering (97)
Marine Engineering (124)
Power Plant Engineering (172)
Textile Engineering (575)
Production Engineering (25)
Satellite Systems Engineering (106)
Engineering AllOther (1379)