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Determine the kind of nonmarine sedimentary deposits that reflects arid environmental conditions
|
The nonmarine environments that reflect the arid environments are sand dunes and evaporites
|
Geobiology/Geobiology Redox Chemistry
|
https://github.com/idrori/stemQ
|
What is the major source of chlorine in seawater? How about sodium? How about sulfate?
|
Looking for specific mention of minerals that supply these major elements to the ocean and how they are delivered. Also, what do they have in common? These are all conservative ions, so they have high concentrations in the world’s ocean today and their concentrations scale with salinity.Weathering and delivery via rivers are the primary source, although additional possible sources such as hydrothermal vents and submarine groundwater discharge should be considered. Apatite, Na- plagioclase-feldspar, and oxidative weathering of pyrite are the main minerals that should be discussed as sources of these conservative ions. NaCl (halite) may be mentioned, but it’s not a true source since it is the recycling of chloride and sodium from evaporites back to seawater. These elements had to originally get into seawater via another pathway.
|
Geobiology/Geobiology Redox Chemistry
|
https://github.com/idrori/stemQ
|
Determine the use of actualism in geology to interpret ancient rocks with the help of some general examples.
|
Actualism is a concept used by geologists to interpret the ancient rocks. For example, geologists can assume that ancient eocks are of volcanic orign as they closelt resemble those forming today by volcanic eruptions of molten rock.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the formation of an ion from uncharged atom.
|
An uncharged atom consists of an equal number of protons and electrons. When an atom loses or gains the electrons, ir becomes an ion
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the conditions that favor the preservation of fossils such as soft parts of the ancient organism within the sediment.
|
Low permeability of oxygen in sediments, inorganic materials that fill the spaces left inside the cell wall, formation of replicas of imprints are some conditions that favour the preservation of soft parts as fossils within the sediment
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the reason for more often use of term food web instead of the food chain for species in a community.
|
In the food chain, each level consists of single specieswhereas in food web several species occupy a single level. That is the reason that food web is commonly used in place of food chain
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the type of stratigraphic correlation that geologists undertake
|
Lithologic correlation and temporal correlation are the two kinds of stratigraphic correlation that geologists undertake
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the geographic patterns observed by chrles darwin that indicate the origin of certain species from their descendants
|
THe difference in pattern and sizes of beaks of finches on the galpagos islands and the variation in the size as well as the pattern of shell of toroise present in different regions of galpagos islands suggested darwin that some organisms descend from others.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the evidence which supports the idea that continents have moved over Earth's surface.
|
The coast on the two sides of atlantic ocean fit together just like two seperated parts of jigsaw puzzle,the similarity between the fauna of two lands, and the presence of similar fossil flora on widely seperated landmasses are some evidence which supports the idea that continents have moved over earth's surface.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine The term ‘Precambrian shield’ and the place where it is present in North America.
|
The precambrian shield is a large precambrian of craton that is exposed to the surface of the earth.In North America, a precambrian shield is present in Canada.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the way in which basic features of Wopmay orogen are typical of orogenic belts.
|
The wopmay orogen, which is typical of orogenic belts, was formed by teh deposition of quartz sandstone, carbonate rocks, mudstone, and flysch deposits.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the reason behind the profound geological knowledge about life that colonized early Paleozoic seafloors as compared to the life that floated and swam above seafloors.
|
The presence of immense fossil record helped the geologists to know more about the life forms that colonized early Paleozoic seafloors
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the important ways in which the invertebrate life changed between Ordovician time and Devonian time.
|
The mass extinction in the ocean during Ordovician Period, lead the the development of more advanced reef builders and swimming predators. At the end of devonian period, plants spread over the land and vertebrate animals invaded the terrestrial ecosystem.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the The reason behind the repeated expansion and contraction of shallow seas over the midcontinent United States during Late Carboniferous time.
|
The continual expansion and contraction of glaciers in Gondwanaland caused the expansion and contraction of shallow seas over the midcontinent United States
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the important groups of Paleozoic marine animals that were absent from Triassic seas.
|
The important groups of Paleozoic marine animals that were absent from Triassic seas are fusulinid foraminifera, Lacy bryzoans, Rugose and tabulate corals, and Trilobites.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the causes of the occurrence of abundant chalk in the Cretaceous time.
|
The chalk was abundant during the Cretaceous period due to the presence of coccolithophores in the warm sea.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the The groups of the animals that played a major role in the late Cretaceous period but were absent in the Paleocene world.
|
Ammonoids, rudist, and marine reptiles were common during the Cretaceous period, but these organisms became extinct in the Paleogene world.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the ways in which mammals become modernized during the Neogene Period
|
During the neogen period, the spread of grassy woodlands resulted in the evolution of many animal species. The evolution of animal species provided a way for mammals to become modernized during the Neogene Period.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the process through which great lakes were formed in the past.
|
Great lakes were formed due to melting of glaciers and erosion of ice sheet of North America. The melted water drained into the depression and contributed to the formation of the lake.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Determine the major groups of Eukarya that are of great significance in the fossil record.
|
Living things fall into three large groups: Archaea, Bacteria, and Eukarya. The first two have prokaryotic cells, and the third contains all eukaryotes. A relatively sparse fossil record is available to help discern what the first members of each of these lineages looked like, so it is possible that all the events that led to the last common ancestor of extant eukaryotes will remain unknown. However, comparative biology of extant organisms and the limited fossil record provide some insight into the history of Eukarya.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Discuss some processes through which global warming can influence the biological pump?
|
The biological pump refers to the creation of chemical gradients in the oceans as a result of biological processes, including primary production, export production, and remineralization. In recitation, we discussed several examples. Any type of nutrient depletion in the surface ocean and concentration increase at depth (~1000 m) would be a good example of the biological pump. Another example discussed in recitation is the dissolved inorganic carbon (DIC) concentration and d13C depth profiles. Carbon is fixed in the surface ocean and remineralized at depth, so there is a lower concentration of DIC in the surface ocean relative to the depths where remineralization is occurring (~1000 m). Similarly, photosynthesizers fix isotopically light carbon and the isotopically light carbon is shuttled to depth via export production. As a result, a carbon isotopic depth gradient is observed where DIC is isotopically heavier in the surface ocean compared to the deeper waters that have input from remineralized organic matter.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Discuss some processes through which global warming can influence the concentration of oxygen in the water column?
|
Marine oxygen concentrations are affected by a combination of physical and biological processes, specifically solubility, air-sea gas exchange, photosynthesis, and remineralization. Warming will decrease oxygen solubility, so the equilibrated surface ocean will hold less oxygen. This is particularly important at higher latitudes, which reportedly will experience the greatest degree of warming, because bottom waters sourced from high latitudes will start off with less oxygen (assuming similar ocean turnover rates). Ocean anoxia and expanded oxygen minimum zones (OMZs) are predicted for the future ocean owing to warming and are thought to have characterized past oceans in greenhouse conditions.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Discuss some processes through which global warming can influence the the production of CaCO3 by phytoplankton
|
The effects of global warming on production of CaCO3 will depend on the source of global warming. Let’s say that the global warming is driven by a pCO2 increase on a geologically rapid timescale (100s to 1000s yrs), as in the modern.Ocean pH should decline as a result of adding more CO2 (an acid). However, CO2 must equilibrate amongst the different carbonate chemistry species (H2CO3*, HCO3-, CO3 2-). Recall the Bjerrum plot for the distribution of C at different pHs given a specified DIC concentration. The species shift left for lower pH. In other words, as pH decreases, less of the DIC will be in the form of carbonate ion (CO3 2-). The solubility product of calcium carbonate depends on Ca2+ concentrations and carbonate ion concentration. A lower concentration on carbonate ion concentration will drive equilibrium away from calcium carbonate precipitation. Therefore, calcification by organisms will become less energetically favorable.
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
What is annamox? Write the reaction for this metabolism.
|
Annamox is anaerobic oxidation of ammonium by nitrate or nitrite.\n (13) NO3- + NH4+ = N 2+ 2H2O\n
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Where in the water column would you expect annamox to occur?
|
In low oxygen zones where nitrate is available. Particularly in oxygen minimum zones (OMZs)
|
Geobiology/Earth System History
|
https://github.com/idrori/stemQ
|
Consider the perfectly competitive market for gasoline. The aggregate demand for gasoline is D(p) = 100 - p while the aggregate supply is S(p) = 3*p. Calculate the equilibrium price and quantity. At this equilibrium, compute the consumer surplus, producer surplus and total surplus.
|
Equilibrium Price = 25
Equilibrium Quantity = 75
Consumer Surplus = 2812.5
Producer Surplus = 937.5
Total Surplus = 3750
|
Principles of Microeconomics/Market Structures
|
https://github.com/idrori/stemQ
|
A monopoly faces market demand Q = 30 - P and has a cost function C(Q) = 1/2*(Q^2). Find the profit maximizing price and quantity and the resulting profit to the monopoly.
|
Profit Maximizing Price = 20
Quantity = 10
Profit = 150
|
Principles of Microeconomics/Market Structures
|
https://github.com/idrori/stemQ
|
Oliver has an endowment of $10,000 that he wants to invest. He can either invest in a bond, which yields 1% or the stock market, which consist of one firm, Amazon. Amazon's stock costs $100 today, and will be worth $400 in one year with probability 0.5 or will drop to $0 with probability 0.5. Oliver’s utility function is U(w) = sqrt(w). Due to institutional regulations, Oliver can invest only in bonds, or only in Amazon, he cannot buy both Amazon stock and bonds. What is Oliver’s utility of buying bonds? What if he invests only in Amazon’s stock? What does he prefer?
|
Utility of buying bonds = ~ 100.5
Utility of investing = 100
Prefer to buy bonds.
|
Principles of Microeconomics/Market Structures
|
https://github.com/idrori/stemQ
|
A uniform pricing monopolist has a cost function C(q) = 1/2*q^2. It faces a market demand of D(p) = p^(-u) where u > 1. Calculate the price elasticity of demand.
|
Optimal Price = (u/(u-1))^(1/(1+u)) = -u
|
Principles of Microeconomics/Market Structures
|
https://github.com/idrori/stemQ
|
Suppose there are only two goods in the world: tea and coffee. In both the US one pound of tea requires 3 hours of labor to produce and one pound of coffee requires 2 hours of labor to produce. A worker can choose to work either in the tea industry or in the coffee industry (skills are completely transferable across industries) and consider the case when the labor market is perfectly competitive, and the market for tea and coffee are also perfectly competitive. Suppose that on the international market, due to the different production functions by different countries, we can trade k pounds of tea for 1 pound of coffee. For what values of k will the US choose to export tea? For what values of k will the US choose to export coffee
|
The US will export coffee for k > 2/3 and the US will export tea for k < 2/3.
|
Principles of Microeconomics/Pricing
|
https://github.com/idrori/stemQ
|
Is the production function: F (L, K) = L^2*K^(1/2) exhibiting constant, increasing or decreasing returns to scale.
|
Increasing Returns to Scale
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
For each of the following production functions:
(a) F (L, K) = L^2*K^(1/2)
(b) F (L, K) = L + L^(1/2)*K^(1/2)
(c) F (L, K) = 2*L + K
State whether the production function exhibits constant, increasing or decreasing returns to scale.
|
IRS, CRS, CRS
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
You manage a factory that produces cans of peanut butter. The current market price is $10/can, and you know the following about your costs: MC(5) = 10, ATC(5) = 6 MC(4) = 4, ATC(4) = 4
A case of food poisoning breaks out due to your peanut butter, and you lose a lawsuit against your company. As punishment, Judge Judy decides to take away all of your profits, and considers the following two options to be equivalent:
i. Pay a lump sum in the amount of your profits.
ii. Impose a tax of $[P - ATC(q^*)] per can since that is your current profit per can, where q^* is the profit maximizing output before the lawsuit.
Judge Judy gives you the option of choosing either plan. Which plan would you choose?
Provide intuition. Hint: a clear diagram may be helpful.
|
Choose to take the tax. The tax would be $4/can. The firm can reduce its quantity to still make a profit.
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
Given the utility function: U(S,C) = 4*ln(S)+6*ln(C), compute the marginal rate of substitution of S for C. Is the marginal rate of substitution increasing or decreasing in S.
|
MRS is decreasing
|
Principles of Microeconomics/Supply/Demand
|
https://github.com/idrori/stemQ
|
Consider a market for skateboards that is in a long-run equilibrium. In this equilibrium, each firm’s short-run and long-run total cost functions are given by: SRTC(q) = q^3 −3*(q^2) +3*q+4 LRTC(q) = 3*q The market demand for skateboards is given by Q_D(P) = 27 - P. What is the equilibrium price in the initial long-run equilibrium?
|
Long run equilibrium price = 3.
LRAC = LRTC(q)/q = 3q/q = 3 = P
Since the market is competitive, the equilibrium price must equal the minimum long-run average cost. Hence, P∗ = 3.
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
Suppose the demand for apples is Q_D = 550 - 50*P and the industry supply curve is Q_S = -12.5 + 62.5*P. Calculate the equilibrium price and quantity.
|
Price = 5
Quantity = 300
|
Principles of Microeconomics/Supply/Demand
|
https://github.com/idrori/stemQ
|
Lauren wants to be a physicist, so she places more weight on her physics test score. Her utility function is given by u(p, e)=0.6 ln(p)+0.4 ln(e). where p is the score on the physics final and e is the score on the economics final. Although she cares more about physics, she is better at economics; for each hour spent studying economics she will increase her score by 3 points, but her physics score will only increase by 2 points for every hour spent studying physics, How many hours should Lauren optimally spend studying physics? How many hour should Lauren study economics?
|
Hours studying economics = 9.6
Hours studying physics = 14.4
|
Principles of Microeconomics/Supply/Demand
|
https://github.com/idrori/stemQ
|
Consider the production of wine and cheese in France and Spain. This table gives the number of necessary hours to produce each (labor is the only input):
France takes 4 hours to produce 1 Kilo of Cheese. Spain takes 6 hours to produce1 Kilo of Cheese. France takes 6 hours to produce 1 Bottle of wine. Spain takes 12 hours to produce 1 Bottle of wine. For each good, which country has an absolute advantage? For each good, which country has a comparative advantage?
|
France has an absolute advantage in both cheese and wine. Spain has a comparative advantage in cheese. France has a comparative advantage in wine.
|
Principles of Microeconomics/Trade
|
https://github.com/idrori/stemQ
|
Chloe consumes only books (x) and video games (y). Her preferences can be represented by the following utility function: U(x,y) = x*(y^2). The price of books is p_x, the price of video games is p_y, and Chloe has an income of m dollars. Compute Chloe's budget constraint.
|
Budget constraint is p_x(x) + p_y(y) ≤ m
|
Principles of Microeconomics/Utility
|
https://github.com/idrori/stemQ
|
Chloe consumes only books (x) and video games (y). Her preferences can be represented by the following utility function: U (x, y) = x*(y^2). Calculate the Marginal Rate of Substitution (at an arbitrary bundle (x, y)).
|
Marginal Rate of Substitution = y/2x
|
Principles of Microeconomics/Utility
|
https://github.com/idrori/stemQ
|
Consider an economy with only one good: food. There are three people in the economy, A, B and C. A has 400 units of food, B has 100 units, and C has only 16 units. All have the same utility, U_i = sqrt(f) for i = A,B,C. The government decides to redistribute food more equally, so it takes 175 units from A and gives them to B. However, the government spoils 79 of these units in transportation, so B ultimately gets only 96 units of food. What is each person's utility level?
|
A's Utility = 15
B's Utility = 14
C's Utility = 4
|
Principles of Microeconomics/Utility
|
https://github.com/idrori/stemQ
|
A consumer’s preferences are represented by the following utility function: u(x,y) = x^(1/2) + y. Obtain the MRS of the consumer at an arbitrary point (x*, y*), where x* > 0 and y* > 0.
|
Marginal Rate of Substitution = (-1/2) * (x^(-1/2))
|
Principles of Microeconomics/Utility
|
https://github.com/idrori/stemQ
|
Draw the Engel curve for video games. Are video games an inferior or a normal good?
|
Video games are a normal good.
|
Principles of Microeconomics/Utility
|
https://github.com/idrori/stemQ
|
Suppose a worker has preferences over consumption and leisure that can be represented by the following utility function: U = ln(c) + ln(l) There are 16 hours per day available for leisure (l) and work (L). The hourly wage is w, and assume that the price of each unit of consumption is $1. Write down the worker’s budget constraint in terms of c and L. Find the optimal consumption and work as a function of w.
|
Optimal consumption = 8w
|
Principles of Microeconomics/Utility
|
https://github.com/idrori/stemQ
|
Determine whether the following statements are True or False. Explain your answer. A government sets a price ceiling for widgets that is below the equilibrium price. This intervention will always decrease the producer surplus, increase consumer surplus and decrease total surplus.
|
False, it might increase or decrease consumer surplus. Price decreases but also quantity decreases. The firm(s) might also exit the market if the price is below average cost which would result in zero consumer surplus.
|
Principles of Microeconomics/Welfare
|
https://github.com/idrori/stemQ
|
Firm X has the following production function F(L, K) = L + K**(2/3). State whether the production function exhibits decreasing returns to scale.
|
nan
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
Suppose an industry has a duopoly structure. Duopolist 1 has a cost function given by: c_1(y_1) = (y_1)^2 for y_1 ≥ 0. Duopolist 2 has a cost function given by: c2(y_2) = 12*y_2 for y_2 ≥ 0. The total output produced in the industry is denoted by: y = (y1 + y2). The inverse demand function for the good produced in the industry is denoted by: p = 100 - y. Find the reaction function of each duopolist.
|
Duopolist 1: (4 * y_1) + y_2 = 100
Duopolist 2: y_1 + (2 * y_2) = 88
|
Principles of Microeconomics/Market Structures
|
https://github.com/idrori/stemQ
|
A firm has a Cobb-Douglas production function q = f(K, L) = K^a * L^(1-a) an d faces wages, w, and rental rate of capital, r. Find the short-run cost curve, C(q), as a function of q and the parameters.
|
Short Run Cost Curve = C(q) = rK_ + wL*(q)
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
Write a program to compute the associated (long run) total, average, and marginal cost curves given the production function f(L,K) = 2*L^(1/4)*K^(1/4).
|
Long Run Average Cost = TC(r, w, Q) = Q^2 w^(1/2) r^(1/2)/2
Average Cost = AC(r, w, Q) = Q w^(1/2) r^(1/2)/2
Marginal Cost = MC(r, w, Q) = Q w^(1/2) r^(1/2)
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
Suppose that there are only two products, computers and automobiles. Automobiles are more labor-intensive (requires relatively more labor) and are produced according to the production function F_A(K, L) = K^(1/3)*L^(2/3) . Computers are more capital intensive (require relatively more capital) and are produced according to the function F_C(K, L) = K^(2/3)*L^(1/3) Suppose that both labor and capital are perfectly mobile across the two industries. That is, workers and capital can switch fluidly from producing computers to producing cars and vice versa. For this problem, assume everything is in perfect competition.
Suppose that the United States has 30 units of labor total and 240 units of capital, and all labor and capital is utilized for production. The price of automobiles is pA = 200 while the price of computers are pc = 100 under autarky. How much labor and capital is used for the production of automobiles under autarky? How much labor and capital is used to produce computers under autarky?
(Hint: Use the condition on wages and prices of capital you found in the previous exercise. In perfectly competitive labor and capital markets, what is the relationship between wages (or price of capital), the production function, and the price of the output goods?)
|
Capital input for automobiles = 80
Labor input for automobiles = 20
Capital input for computers = 160
Labor input for computers = 10
MPL_A is the derivative of a production function for automobiles with respect to labor.
K_A is capital input for automobiles.
200*MPL_A = 100*MPL_C
(400/3)*(K_A/L_A)^(1/3) = (100/3)*((240-K_A)/(30-L_A))^(2/3)
200*MPK_A = 100*MPK_C
(200/3)*(K_A/L_A)^(-2/3) = (200/3)*((240-K_A)/(30-L_A))^(-1/3)
Substitute and solve for
K_A, L_A, K_C, L_C
|
Principles of Microeconomics/Production and Costs
|
https://github.com/idrori/stemQ
|
Mary’s demand curve for food is Q = 10 − 2P. Her price elasticity of demand for food at price P* equals −(2/3). How much is P*?
|
nan
|
Principles of Microeconomics/Savings
|
https://github.com/idrori/stemQ
|
A household has to decide how much to consume during their working age and how much to save for retirement. We will model this as if there were two periods: period 1 is the working age, while period 2 is retirement. Suppose that we can represent the preferences of this household with the utility function U(c1, c2) = ((c_1)^(1-s))/(1-s) + ((c_2)^(1-s))/(1-s) where c_1 is consumption in period 1, and c_2 is consumption in period 2 and s > 0. Buying 1 unit of consumption costs $1 in both periods. Income in period 1 is W dollars and zero during retirement. The household can save at the market interest rate r. Assume that the household gets no utility from leaving any money behind after death. How much of its income will the household consume and how much will it save given the interest rate r?
|
Savings = s = W − c1 = W 1 − 1 1 + (1 + r) 1− σ σ ! = W(1 + r) 1− σ σ 1 + (1 + r) 1− σ σ
|
Principles of Microeconomics/Savings
|
https://github.com/idrori/stemQ
|
Anne consumes only books (x) and video games (y). Her preferences can be represented by the following utility function: U = (x^2)*y. The price of books is p_x, the price of video games is p_y, and Anne has an income of m dollars. Compute Anne's demand for books and video games as a function of p_x, p_y and m.
|
x(p_x, p_y, m) = (2/3) * (m/p_x)
y(p_x, p_y, m) = (1/3) * (m/p_y)
|
Principles of Microeconomics/Supply/Demand
|
https://github.com/idrori/stemQ
|
Xiaoyu spends all her income on statistical software (S) and clothes (C). Her preferences can be represented by the utility function: U(S,C)=4*ln(S)+6*ln(C). Find Xiaoyu's demand functions for software and clothes, Q_S(p_S, p_C, I) and Q_C(p_S, p_C, I), in terms of the price of software (p_S), the price of clothes (p_C), and Xiaoyu's income (I).
|
Q_s(p_s, p_c, I) = (2/5)*(I/p_s)
Q_c(p_s, p_c, I) = (3/5)*(I/p_c)
|
Principles of Microeconomics/Utility
|
https://github.com/idrori/stemQ
|
a) Assuming steady-level flight and no fuel reserves, estimate the range of a B-777 using the information given in the lecture notes (and/or on Boeing’s web page). How well does this compare to the estimates Boeing publishes on their web page?
b) Now assuming that L/D, propulsion system efficiency and final weight are unchanged, estimate the range of a B-777 if the same volume of liquid hydrogen were to be used instead of Jet-A.
|
You get about 18000km using the ratio of the operating empty mass and the max takeoff mass (1.9). The estimate of 18000km is more than 30% too high, but I did neglect the weight of the passengers and their cargo, food (such as it is), and reserve fuel. When these items are taken into account the estimate is within 10% of the published values. To do this I wrote Wfinal=Winitial-Wfuel = Winitial-ρfuel Vfuel. The ratio of the two densities is 0.0875. So the initial weight is only 156,000 kg (144,000kg + 0.0875x137,000kg), and the weight ratio drops to 1.08. Of course the heating value is increased by a factor of 2.8, but it hardly makes up for the reduction in the amount of energy that is carried due to hydrogen’s low density. My estimate for the range is 6100km, a reduction by a factor of three from the case with Jet-A.
|
Unified Engineering 1 and 2/Unified Engineering
|
https://github.com/idrori/stemQ
|
Convert the following base 10 numbers into 8-bit 2’s complement notation 0, -1, -12
|
To Compute 0
0 = 00000000
To Compute –1
Step 1. Convert 1 to binary 00000001
Step 2. Flip the bits 11111110
Step3. Add 1 11111111
Therefore –1 = 11111111
To Compute –12
Step 1. Convert 12 to binary 00001100
Step 2. Flip the bits 11110011
Step3. Add 1 11110100
Therefore –12 = 11110100
|
Unified Engineering 1 and 2/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Write an algorithm to implement the subtraction operation for two positive integers in assembly language.
|
1. Let the numbers be A, B and the operation be A-B 2. Convert A into binary 3. Convert B into binary 4. Compute 2’s complement of B i. Invert the bits in B using B xor 11111111 ii. Add 1 to B 5. Add A and the 2’s complement of B.
|
Unified Engineering 1 and 2/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Write an Ada95 program to accept a date in the Date/Month/Year format. Accept each of the inputs separately. Display the date in all three formats as shown below. Turn in the hard copy of your algorithm and code listing, and an electronic copy of your code.
i. 19/9/2003 (Date, Month, Year)
ii. 19 September 2003
iii. 19.IX.2003
Hint: Use Enumerations to represent the month. Note: The enumerations range from 0 to (number_of_elements_in_Enumeration –1).
|
1. Use a subtype to represent the numbers for months
2. Use an enumeration to represent the named months
3. Use an enumeration to represent the roman months
4. Get the inputs from the user
5. Convert the month into roman and named formats using
a. New_Type_Package’Val(Month_Type’Pos(Month) –1);
6. Display the months in all three formats to the user.
|
Unified Engineering 1 and 2/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
What are the First and Last values of the following data types
a. Integer
b. Float
c. Character
d. Boolean
|
a. Integer
Integer’First = -2147483648 Integer’Last = 2147483647
b. Float
Float’First = -3.40282E+38 Float’Last = 3.40282E+38
c. Character Character’First =
Character’Last =
Note that both the character values are control character and hence do not get printed on the screen. The position values are 0, 255
d. Boolean
Boolean’First = FALSE
Boolean’Last = TRUE
|
Unified Engineering 1 and 2/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Consider the system of equations
x+ y−2z=−1 x + 4y + 2z = 5 x+y−z=0
Fall 2003
Solve for x, y, and z, in three separate ways. The goal of part (1) is to practice solving systems of equations, so that when you get to part (2), you will have a fair basis of comparison.
(a) Determine x, y, and z using (symbolic) elimination of variables. (b) Determine x, y, and z by Gaussian reduction.
(c) Determine x, y, and z using Cramer’s rule.
|
x + y − 2z = −1 x + 4 y + 2z = 5 x+y−z=0
x + y − 2 z = −1 x + 4y + 2z = 5 2 x + 5 y = 4
−2(3x + 6 y = 5) 3(2x + 5y = 4) 3y = 2
3x + 6(2 / 3) = 5 3x = 1
1/ 2 + 2 / 3 − z = 0
1.b
x + 4 y + 2 z = 5 2(x + y − z) = 0 3x + 6 y = 5
y=2/3
x =1/3
z=1
|
Unified Engineering 1 and 2/Signals and Systems
|
https://github.com/idrori/stemQ
|
Solve the following recurrence equation using the iteration method. Show all the steps in your derivation.
c n=1 T(n)= n
aT b√+cn n>1 ↵
Where a,b,c >=1.
|
Substitute the value of T(n) from the recurrence equation: aT(n/b) + cn
⇒ a(aT((n/b)/b) + c(n/b)) + cn
⇒ a2T(n/b2) + cn(a/b) + cn
⇒ a2T(n/b2) + cn((a/b) + 1)
⇒ a2(aT((n/b2)/b) + cn/b2) + cn((a/b) + 1)
⇒ a3T(n/b3) + cn(a2/b2) + cn((a/b) + 1)
⇒ a3T(n/b3) + cn((a2/b2)+ (a/b )+ 1) ...
⇒ akT(n/bk) + cn((ak-1/bk-1)+ (ak-2/bk-2)+ ... + (a2/b2)+ (a/b) + 1)
When k = logb n, ⇒ n = bk
T(n) = akT(1) + cn(ak-1/bk-1 + ... + a2/b2 + a/b + 1)
= akc + cn(ak-1/bk-1 + ... + a2/b2 + a/b + 1)
= cak + cn(ak-1/bk-1 + ... + a2/b2 + a/b + 1)
= cnak/bk + cn(ak-1/bk-1 + ... + a2/b2 + a/b + 1) = cn(ak/bk + ... + a2/b2 + a/b + 1)
|
Unified Engineering 1 and 2/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Define the term polymer and list three engineering polymers.
|
A polymer is a large molecule made up of smaller repeating units (mers). Typically polymers have carbon “backbones” with side groups consisting of other organic atoms (C, H, O, N). Engineering polymers: polyethylene, polystyrene, epoxy
|
Unified Engineering 1 and 2/Materials and Structures
|
https://github.com/idrori/stemQ
|
Define a thermoplastic and a thermoset.
|
A thermoplastic softens dramatically with increasing temperature. A thermoset does not. Thermoplastics consist of long polymer chains with no covalent cross-links between the chains. The chains are bonded together by Van der Waals bonds. Thermosets have covalent crosslinks between the chains.
|
Unified Engineering 1 and 2/Materials and Structures
|
https://github.com/idrori/stemQ
|
What is the glass transition temperature?
|
The glass transition temperature is the temperature at which the Van der Waals bonds melt. It is the temperature at which the elastic properties drop dramatically in thermoplastics.
|
Unified Engineering 1 and 2/Materials and Structures
|
https://github.com/idrori/stemQ
|
Explain the change in moduli of polymers at the glass transition temperature.
|
The Van der Waals bonds “melt” at this temperature, i.e. the thermal vibration exceeds the ability of the bonds to hold the molecules together. Thermoplastics rely on Van der Waals bonds for their elastic response at low temperatures. If these bonds are removed,then the polymer behaves viscoelastically, with the elastic component
coming from entanglements between the polymer chains.
|
Unified Engineering 1 and 2/Materials and Structures
|
https://github.com/idrori/stemQ
|
How would you increase the modulus of a polymer?
|
Introduce covalent cross-links.
Increase degree of crystallinity. Increase alignment of polymer chains.
|
Unified Engineering 1 and 2/Materials and Structures
|
https://github.com/idrori/stemQ
|
What does it mean for a process to be quasi-equilibrium?
|
A process is quasi-equilibrium if the time rate of change of the process is slow relative to the time it takes for the system to reach thermodynamic equilibrium.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
Why is it necessary that a system be quasi-equilibrium (i.e. quasi-static) before applying many of the thermodynamics relations to that system?
|
If the system is not in equilibrium, then different parts of the system exist at different states at the same time and it is not possible to define one “state” of the system. Since many of the thermodynamic relations relate to the state of the system, it is necessary that a state can be defined for the system before applying them.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
Explain how a refrigerator works in terms of energy, heat and work.
|
The objective of a refrigerator is to lower the internal energy of a body at low temperature (the food) and transfer that energy to the higher temperature surroundings (the room the refrigerator is in). It requires work (typically in the form of electrical energy) to do this. Most refrigerators employ a thermodynamic cycle with refrigerant circulating around a loop. As the refrigerant circulates around the loop, its internal energy (and temperature) is alternately raised and lowered by a series of devices. First the internal energy is lowered either by passing through a small turbine or through an expansion valve. In these devices, work is done by the refrigerant so its internal energy is lowered. The internal energy is lowered to a point where the temperature of the refrigerant is lower than that of the air in the refrigerator. A heat exchanger is used to transfer energy from the air (and food) in the refrigerator to the cold refrigerant (energy transferred by virtue of a temperature difference only = heat). This lowers the internal energy of the air/food and raises the internal energy of the refrigerant. Then a pump or compressor is used to do work on the refrigerant adding additional energy to it and thus further raising its internal energy. Electrical energy is used to drive the pump or compressor. The internal energy of the refrigerant is raised to a point where its temperature is hotter than the temperature of the room. The refrigerant is then passed through a heat exchanger (the coils at the back of the refrigerator) so that energy is transferred from the refrigerant to the surroundings. As a result, the internal energy of the refrigerant is reduced and the internal energy of the surroundings is increased. It is at this point where the internal energy of the food and the energy used to drive the compressor or pump are transferred to the surroundings. The refrigerant then continues on to the turbine, repeating the cycle.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
For a system composed of a small mass of gas passing through a rocket nozzle, describe the physical implications of an adiabatic, quasi-equilibrium (i.e. quasi- static) process.
|
Such an assumption would imply that the mass of gas passes through the nozzle too fast for significant heat transfer to occur, but at a rate which is slow compared to the time it takes the small mass of gas to come to thermodynamic equilibrium.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
For a thermodynamic cycle involving an ideal gas, what is the relationship between work, shaft (or external) work and flow work when these quantities are calculated for the cycle as a whole?
|
w=ws +wf
wf = R(∆T) , only a function of the state of the system. Since the system returns to its initial state when completing one loop around the cycle, then wf=0 for a cycle and w=ws for a cycle.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
For a thermodynamic cycle involving an ideal gas, what is the relationship between heat and work when calculated for the cycle as a whole?
|
∆u = q – w
u is a property and a function of the state of the system. Therefore ∆ucycle = 0 since the system returns to its initial state when completing one loop around the cycle. So
wcycle=qcycle
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
What is the physical meaning of enthalpy and for what kinds of systems is it useful and why?
|
Enthalpy is the amount of energy that is transferred across a system boundary by a moving flow. This energy is composed of two parts: the internal energy of the fluid (u) and the flow work (pv) associated with pushing the mass of fluid across the system boundary. Because enthalpy is a measure of the energy that is transferred across a system boundary by a flow, it is most useful for flow processes involving open systems, e.g. applications of the steady flow energy equation.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
Which terms in the first law of thermodynamics depend on path? Explain why the dependence on path is important for the design of heat engines.
|
Heat and work are path dependent. Energy is not path dependent, it is a function of the state of the system. The implication of path dependence for heat engines is that it is possible take a system from one thermodynamic state to another via different paths (i.e. processes). These processes , which are defined by the engineer, have different amounts of heat and work, and thus result in difference performance for the heat engine.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
Explain the difference between heat and temperature.
|
Heat is the transfer of energy across a system boundary by virtue of a temperature difference only. It is measured in Joules. Temperature is a thermodynamic property and a function of the state of the system. It is measured in Kelvin.
|
Unified Engineering 1 and 2/Thermodynamics
|
https://github.com/idrori/stemQ
|
Derive an equation for the range of a battery-powered aircraft in steady-level flight. Express the range in terms of L/D, propulsion system efficiency, battery mass and heating value, and aircraft weight. Estimate the range of a B-777 if the fuel was taken out and replaced with its equivalent weight in batteries.
|
The key with a battery-powered aircraft is that its mass does not change as it burns the energy. This makes the range equation more straightforward.
mb ⋅ h = energy available in the battery ( J )
T⋅uo =rateof energyusagetoovercomedrag(J/s)
ηoverall
time of flight = mb ⋅ h
T ⋅ uo ηoverall
(s)
Rangeof flight=umb⋅h
(m)
or
o T⋅u o ηoverall
Range of flight = mb ⋅h⋅ηoverall = mb ⋅h⋅ηoverall L (m) T WD
With mb = 137,000kg, h=2.5MJ/kg, W=(275,000kg)(9.8m/s2)=2695kN, I calculate the range to be: 820km. As you can see, the low energy density of the battery is a disaster for range—it is reduced by a factor of more than 20 relative to the Jet-A powered model.
|
Unified Engineering 1 and 2/Unified Engineering
|
https://github.com/idrori/stemQ
|
Draw a thermodynamic cycle on p-v and T- v diagrams consisting of
Leg 1-2: adiabatic expansion
Leg 2-3: constant volume heat addition Leg 3-4: constant pressure expansion Leg 4-1: isothermal compression
Assume that all processes are quasi-static and involve an ideal gas.
|
nan
|
Unified Engineering 1 and 2/Unified Engineering
|
https://github.com/idrori/stemQ
|
Convert ‘2 + 3 = 5’ into ASCII
|
‘2’ - 50 ‘ ’ - 32 ‘+’ - 43 ‘ ’ - 32 ‘3’ - 51 ‘=’ - 61 ‘5’ - 53
|
Unified Engineering 1 and 2/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Convert the following binary numbers into hexadecimal. 0000 1111 0000 1111
|
0F0F
|
Unified Engineering 1 and 2/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Write an algorithm to check if a user entered string is a palindrome.
Assume:
i. Maximum string length is 80 characters
ii. The actual string length is input dependent
|
Get input string and length from the user. Set Flag to True
For I in 1 .. Length/2 loop
If String(I) /= String(Length – I+1) then Display ‘Input_String not a Palindrome” Set Flag to False
If Flag = True then
Display “Input String is a Palindrome”
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Compare and contrast stacks and queues.
|
Stacks and Queues are subclasses of Linear Lists.
Stacks
A Stack is an ordered (by position, not by value) collection of data (usually homogeneous), which maintains a Last-In-First-Out order. All access to a stack is restricted to one end of the list, called the top of stack. Visually, picture a stack of books, coins, plates, etc. Insertion and Deletion both take place at the top of the stack. The following operations are defined for stacks:
Operation
Description
Initialize
Initialize internal structure; create empty stack
Push
Add new element to top of stack
Pop
Remove top element from stack
Empty
True iff stack has no elements
StackTop
Returns copy of top element of stack (without popping it)
Size
Returns number of elements in the stack
Queues
A queue is an ordered (by position, not by value) collection of data (usually homogeneous), which maintains the First-In-First-Out order of elements. Insertion of elements is carried out at the ‘Tail’ of the queue and deletion is carried out at the ‘Head’ of the queue. The following operations are defined for queues:
Operation
Description
Initialize
Initialize internal structure; create an empty queue
Enqueue
Add new element to the tail of the queue
Dequeue
Remove an element from the head of the queue
Empty
True iff the queue has no elements
Full
True iff no elements can be inserted into the queue
Size
Returns number of elements in the queue
Display
Display the contents of the Queue
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
What are doubly linked lists? What is the record declaration for a node in a doubly linked list?
|
Doubly linked lists have two pointers instead of the single pointer seen in singly linked lists. The pointers point to both the previous node in the list as well as the next node in
the list.
type Listnode is record
Element : Elementtype;
Next : Listptr;
Prev : Listptr; -- this is the change made to singly linked lists
end record;
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Write an algorithm to insert a node into a sorted doubly linked list. Use a diagram to show the sequence of operations that have to be performed to carry out the insertion step.
|
Preconditions:
1. User passes the list (called List) and the element to be inserted (called Element) to
the insert procedure
2. List is already sorted
Postconidtions:
1. Procedure returns the list with the element inserted in the correct position
2. List remains sorted
Algorithm:
Create three temporary Listptrs Current, Previous and NewNode Previous := null
Current := List.Head;
NewNode := new Listnode;
NewNode.Element := Element
Loop
exit when Current = Null
exit when Current.Element > Element Previous := Current;
Current := Current.Next;
NewNode. Next := Current; NewNode.Prev:= Previous; If Previous = null
L.Head := NewNode else
Previous.Next := NewNode If Current /= null
Current.Prev := NewNode;
Return List
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
What are the best case and worst case computation complexity of: a. Inserting a node into an unsorted singly linked list and b. Inserting a node into a sorted singly linked list
|
In the case of a sorted linked list, the list has to be traversed to find the right position. The list traversal takes O(n) in the worst case.
Best case execution time is O(1) if the element being inserted is the smallest element in the list (list in ascending order)
Worst case execution time is O(n) if the element being inserted is the largest element in the list (list in ascending order)
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Define a recursive binary search algorithm.
|
If lb > ub
Return -1
else
Mid := (lb+ub)/2
If Array(Mid) = element Return Mid
Elsif Array(Mid) < Element
Return Binary_Search(Array, mid+1, ub, Element)
Else
Return Binary_Search(Array, lb, mid-1, Element)
End if End if
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
What is the Big-O complexity of:
a. Heapify function
b. Build_Heap function
c. Heap_Sort. Show all the steps in the computation of the Big-O complexity.
|
a. Heapify function
A heap is an array that satisfies the heap properties i.e., A(i) ≤ A(2i) and A(i) ≤ A(2i+1).
The heapify function at ”i‘ makes A(i .. n) satisfy the heap property, under the assumption that the subtrees at A(2i) and A(2i+1) already satisfy the heap property.
Heapify function Cost
Lchild := Left(I); c1 Rchild := Right(I); c2 if (Lchild <= Heap_Size and Heap_Array(Lchild) > Heap_Array(I)) c3
Largest:= Lchild; c4 else c5 Largest := I; c6
if (Rchild <= Heap_Size) c7 if Heap_Array(Rchild) > Heap_Array(Largest) c8 Largest := Rchild; c9
if (Largest /= I) then c10 Swap(Heap_Array, I, Largest); c11 Heapify(Heap_Array, Largest); T(2n/3)
T(n) = T(2n/3) + C‘
= T(2n/3) + O(1)
a = 1, b = 3/2, f(n) = 1, therefore by master theorem,
T(n) =O(nlogbalogn) = O (nlog3/2 1 logn)
= O(1 * log n) = O(log n)
The important point to note here is the T(2n/3) term, which arises in the worst case, when the heap is asymmetric, i.e., the right subtree has one level less than the left subtree (or vice-versa).
b.
Build_Heap function
Code
Heap_Size := Size;
for I in reverse 1 .. (Size/2) loop
Heapify(Heap_Array, I); end loop;
Therefore T(n) = c1+ n/2+1 + (n/2)log n + n/2 = (nlog(n))/2 + n + (c1+1)
Cost t(n)
c1
n/2+1 (n/2) log n n/2
Simplifying
=> T(n) = O(n log(n) )
c. Heap_Sort
Heap Sort
Build_Heap(Heap_Array, Size); for I in reverse 2.. size loop Swap(Heap_Array, 1, I);
Heap_Size:= Heap_Size -1; Heapify(Heap_Array, 1);
T(n) = 2 O(nlogn) + (c1+c2+1)n - O(log n) + = 2 O(nlog n) - O(log n) + c‘n
Simplifying,
=> T(n) = O(nlogn)
Cost t(n)
O(nlogn))
n
c1(n-1) c2(n-1) O(log n)(n-1)
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
For each of the following Laplace transforms, find the inverse Laplace transform. G(s)=(3s6^2 +3s−10)/(s^2 − 4), Re[s]>2
|
G(s) = 3+ 2 + 1 , Re[s]>2 s−2 s+2
We can take the inverse LT by simple pattern matching. The result is that g(t) = 3δ(t) + (2e2t + e−2t) σ(t)
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
Consider an aircraft flying in cruise at 250 knots, so that
v0 = 129 m/s
Assume that the aircraft has lifttodrag ratio
L0 =15 D0
Spring 2004
Then the transfer function from changes in thrust to changes in altitude is
G(s)= 2g 1 (1)
mv0 s(s2 +2ζωns+ωn2)
where the natural frequency of the phugoid mode is
ωn = √2 g (2) v0
the damping ratio is
ζ=√ 1 (3)
2(L0 /D0 )
and g = 9.82 m/s is the acceleration due to gravity. The transfer function can be
normalized by the constant factor 2g , so that mv0
G ̄(s) = 1
s(s2 +2ζωns+ωn2)
is the normalized transfer function, corresponding to normalized input u(t)= 2gδT
mv0. Find the impulse response corresponding to the transfer function G(s),
using partial fraction expansion and inverse Laplace techniques. Hint: The poles of the system are complex, so you will have to do complex arithmetic.
|
From the problem statement,
√ 9.82 m/s2
ωn = 2 129 m/s = 0.1077 r/s
ζ = √ 1 2(L0/D0
= √ 1 = 0.0471 2 · 15
Therefore,
G ̄ ( s ) =
The roots of the denominator are at s = 0, and
1
s (s2 + 0.01015s + 0.0116)
s = −0.01915 ±
= −0.005075 ± 0.1075j
√
0.010152 − 4 · 0.0116 2
So
G ̄ ( s ) = 1
s (s − [−0.005075 + 0.1075j]) (s − [−0.005075 − 0.1075j])
Use the coverup method to obtain the partial fraction expansion
86.283 −43.142 + 2.036j G(s) = s + s − [−0.005075 + 0.1075j]
+ −43.142 − 2.036j
s − [−0.005075 − 0.1075j]
Taking the inverse Laplace transform (assuming that g ̄(t) is causal), we have g ̄(t) =86.283σ(t)
+ (−43.142 + 2.036j)e(−0.005075+0.1075j)t + (−43.142 − 2.036j)e(−0.005075−0.1075j)t
Therefore,
g ̄(t) = σ(t) [86.283 + 2e−0.005075t (−43.142 cos ωdt − 2.036 sin ωdt)]
= σ(t) [86.283 + (−86.284 cos ωdt − 4.072 sin ωdt) e−0.005075t] where ωd = 0.1075 r/s.
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
For each signal below, find the bilateral Laplace transform (including the region of convergence) by directly evaluating the Laplace transform integral. If the signal does not have a transform, say so. g(t) = sin(at) σ(-t)
|
To do this problem, expand the sinusoid as complex exponentials, so that
�eajt − e−ajt �
g(t) = 2j σ(−t)
Therefore, the LT is given by
�0 �eajt−e−ajt�−st G(s)= 2jedt
−∞
For the LT to converge, the integrand must go to zero as t goes to −∞. Therefore, the integral converges only for Re[s] < 0. The integral is then
g(t) = sin(at)σ(−t)
�0 �eajt−e−ajt�−st G(s) 2jedt
=1�1−1� 2j −s+aj −s−aj
= −a , Re[s] < 0 s2 + a2
−∞
1 � 1 (aj−s)t�0
1 (−aj−s)t�0 � − −s − aj e �
= 2j −s + aj e � �−∞
�−∞
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
Define a robust algorithm to carry out integer division using repeated subtraction.
Your algorithm accepts two integers and returns the quotient and the remainder. Hint: What are the preconditions and postconditions of your algorithm?
|
Precondtions: Two integers x,y y is non-zero
Algorithm:
Set R to absolute_value(x)
Set Q to zero
While R >= absolute_value (y)
Increment Q
R := R- absolute_value(y) If either x or y are negative
If both x and y are negative Set R to –R
else
if x is negative
Set R to –R Set Q to –Q
Display Q and R
Postconditions: Q contains the quotient R contains the remainder
x = Q*y + R, abs(R) < abs(Q)
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
What is the cyclomatic complexity of the code fragment shown below? loop
exit when Flag := True;
if A < 100 and B > 200 then if A > 50 then
Sum := Sum +2; else
Sum := Sum +1; end if;
else
if B < 300 then
Sum:= Sum -1; else
Sum := Sum -2; end if;
end if; end loop;
|
11 Nodes, 14 edges => Cyclomatic complexity = 5
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
What is the minimum number of test cases needed to test the fragment of code
shown below? Justify your answer.
if A < 100 and B > 200 then if A > 50 then
Sum := Sum +2; else
Sum := Sum +1; end if;
else
if B < 300 then
Sum:= Sum -1; else
Sum := Sum -2; end if;
end if;
|
4 test cases
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
n class, you learned about a smoother, with transfer function
G1(s) = −a2 (s−a)(s+a)
The smoother is an example of a lowpass filter, which means that it tends to attenuate highfrequency sine waves, but “pass” lowfrequency sine waves. Unfortunately, the smoother is noncausal, which means that it can’t be implemented in real time. A similar causal lowpass filter is
G2(s) = a2 (s+a)2
In this problem, you will compare these two lowpass filters, to see how they affect sinusoidal inputs. Consider an input signal
u(t) = cos ωt
1. Find the transfer function, G1(jω), as a function of frequency, ω.
|
G1( jω) = −a2
( jω − a)( jω + a)
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
Explain why the noncausal filter is preferred in signal processing applications where it can be applied.
|
The non-causal filter produces no phase shift. Therefore, setting the input is easier and the waveform will arrive at the next stage on time. Signals with multiple frequency components would be jumbled due to the variance of pure phase shift at each frequency of the causal filter. The non-causal filter will scale each frequency but produce no phase shift, thereby making an effective multiple frequency low-pass filter.
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
Using truth tables, show that not A 〈 not B) = not(A + B)
|
nan
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Convert the following expression into product of sum form:
not A〈not B〈not C+not A〈B〈C+A〈B〈not C+A〈not B〈C
|
(A + B + not C) 〈(A + not B + C) 〈 (not A + not B + not C) 〈 (not A + B + C)
|
Unified Engineering 3 and 4/Unified Computers and programming
|
https://github.com/idrori/stemQ
|
Consider the signal
g(t) = (1 + |t|)e−|t|
1. Plot the signal. Do you expect the signal to have a “good” durationbandwidth
product, meaning that the product is close to the lower bound?
|
The signal is very smooth, almost like a Gaussian. Therefore, I expect that the duration bandwidth product will be close to the theoretical lower bound.
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
Consider the signal g(t) = (1 + |t|)e−|t|. Find the duration of the signal, Δt.
|
Δt=2 √(7/5)
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
Consider the signal
g(t) = (1 + |t|)e−|t|. Find the bandwidth of the signal, Δω. You may want to use the time domain formula for the bandwidth.
|
Δω = 2/√5
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
Consider the signal g(t) = (1 + |t|)e−|t|. How close is the answer to the theoretical lower bound? Explain why the answer is or is not close to the bound.
|
The duration bandwidth product is ΔtΔω = 4 √7/5 which is very close to the theoretical lower limit of 2. This is not surprising, since the shape of g(t) is close to a gaussian.
|
Unified Engineering 3 and 4/Signals and Systems
|
https://github.com/idrori/stemQ
|
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