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Computer Networks

4. (P10, Page72)Consider a packet of length L that begins at end system A and travels over three links to a destination end system.These three links are connected by two packet switches. Let d;, si, and R¡ denote the length, propagation speed, and the transmission rate of link i, for i=1,2,3. The packet switch delays each packet by d proc- Assuming no queuing delays, in terms of d;, si, Ri, (i=1,2,3), and L, what is the total end-to-end delay for the packet? Suppose now the packet is 1,500 bytes, the propagation speed on all three links is 2.5*10$m/s, the transmission rates of all three links are 2 Mbps, the packet switch processing delay is 3 m sec, the length of the first link is 5,000 km, the length of the second link is 4,000 km, and the length of the last link is 1,000 km. For these values, what is the end-to-end delay?

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Computer Networks

Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when transmitting, but each user transmits only 10 percent of the time. (a) When circuit switching is used, how many users can be supported?For the remainder of this problem, suppose packet switching is used. Find the probability that a given user is transmitting.Suppose there are 120 users. Find the probability that at any given time, exactly n users are transmitting simultaneously. (Hint: Use the binomial distribution.)Find the probability that there are 21 or more users transmitting simultaneously.

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Kinematics of Machines

• 2-40 Water is being heated in a closed pan on top of a range while being stirred by a paddle wheel. During the process, 30 kJ of heat is transferred to the water, and 5 kj of heat is lost to the surrounding air. The paddle-wheel work amounts to 500 N:m. Determine the final energy of the system if its initial energy is 12.5 kJ.

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Thermodynamics

The figure below shows a gas contained in a vertical piston-cylinder assembly. A vertical shaft whose cross-sectional area is 0.8 cm? is attached to the top of the piston. Determine the magnitude, F, of the force acting on the shaft, in N, required if the gas pressure is 3 bar. The masses of the piston and attached shaft are 24.5 kg and0.5 kg, respectively. The piston diameter is D = 5 cm. The local atmospheric pressure is 1 bar. The piston moves smoothly in the cylinder and g = 9.81 m/s?.Using multiple attempts will impact your score.20% score reduction after attempt 1As shown in the figure below, air is contained in a vertical piston-cylinder assembly such that the piston is in static equilibrium. The atmosphere exerts a pressure of 14.7 Ibf/in. on top of the 8-in-diameter piston. The absolute pressure of the air inside the cylinder is 16 lbf/in. The local acceleration of gravity is g-32.2 ft/s.Determine (a) the mass of the piston, in Ib, and (b) the gage pressure of the air in the cylinder, in psig,

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Probability

Assume that females have pulse rates that are normally distributed with a mean of u=73.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below.a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 79 beats per minute.b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 79 beats per minute.c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?O B. Since the mean pulse rate exceeds 30 , the distribution of sample means is a normal distribution for any sample size.O A. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.O D. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.O C. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.

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Kinematics of Machines

2- Problem 5.8: . A 1130-kg car is held in place by a light cable on a very smooth(frictionless) ramp, as shown in Fig. E5.8. The cable makes an angle of 31.0° above the surface of the ramp, and the ramp itself rises at 25.0° above the horizontal. (a) Draw a free-body diagram for the car. (b) Find the tension in the cable. (c) How hard does the surface of the ramp push on the car?

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Thermodynamics

3-51 A piston-cylinder device contains 0.005 m of liquid water and 0.9 m³ of water vapor in equilibrium at 600 kPa. Heat is transferred at constant pressure until the temperature reaches 200°C.(a) What is the initial temperature of the water?(b) Determine the total mass of the water.(c) Calculate the final volume.(d) Show the process on a P-V diagram with respect to saturation lines.

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Thermodynamics

3.19. An ideal gas initially at 600 K and 10 bar undergoes a four-step mechanically reversible cycle in a closed system. In step 12, pressure decreases isothermally to 3 bar; instep 23. pressure decreases at constant volume to 2 bar; in step 34, volume decreases at constant pressure; and in step 41, the gas returns adiabatically to its initial state.Take Cp = (7/2)R and Cy = (5/2)R.(a) Sketch the cycle on a PV diagram.(b) Determine (where unknown) both T and P for states 1, 2, 3, and 4.\text { (c) Calculate } Q, W, \Delta U, \text { and } \Delta H \text { for each step of the cycle. }

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Data Science

Ques 6 Your goal is to navigate a robot out of a maze. The robot starts in the center of the maze facing north. You can turn the robot to face north, east, south, or west. You can direct the robot to move forward a certain distance although it will stop after hitting a wall.a) Formulate this problem. This means you will have to describe initial state, goal test,successor function. and cost function. Successor function is a description of the robots successive actions after the initial state.We’ll define the coordinate system so that the center of the maze is at (0, 0), and the maze itself is a square from (-1,–1) to (1, 1)

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Thermodynamics

2-45 A gas is contained in a vertical, frictionless piston cylinder device. The piston has a mass of 3.2 kg and across-sectional area of 35 cm². A compressed spring above the piston exerts a force of 150 N on the piston. If the

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Chemical Process Calculations

2.17.6: Two distillation columns with ethanol, butanol, and propanol.

Two distillation columns, which are overseen by engineers Gianna and Peter, separate three components. A liquid mixture enters the first column at 536 kg/s and contains 35.0 mass % ethanol (C₂H5OH), 15.0 mass % propanol (C3 H7 OH), and the balance butanol (C4 H9 OH). The bottom product stream of the first column contains 93.1 mass % B and no E, and 95.1% of the B in the feed stream is recovered in the bottom product stream. The overhead product of the first column is used as the feed stream to the second column. The overhead product from the second column contains 92.1% of the E inthe feed to this column. The composition of the overhead product stream is 91.5 mass % E and the balance P.
Find the component mass flow rates (kg/s) exiting in the overhead product of the first distillation column. Stream numbering is same as PFD for question 1.

m3, EEx: 284 kg/s=

m3,p = Ex: 74.3kg/s

m3, B =Ex: 15.7kg/s

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Chemical Process Calculations

2.17.7: Two distillation columns with three components.

A pair of distillation columns are being monitored by Beatrix and Enrico. Benzene (B), toluene (T), and xylene (X) are fed to the first distillation column. The overhead product of the first column contains only benzene and toluene. Toluene is fed to the first column at 1020 mol/hr while 74.4% of the benzene fed to the first column ends up in the overhead product. The stream exiting the bottom of the first column has a flow rate of 1590 mol/hr with 28.5 mol % benzene, 23.8 mol% toluene, and the rest xylene. The bottoms product from the first column is fed to a second distillation column. Pure xylene exits the bottom of the second column while the overhead product contains only benzene and toluene.
Determine the following three unknowns.

Flow rate of xylene exiting the second column = Ex: 515 mol/hr

Mole fraction of toluene exiting the second column = Ex: 0.582

Flow rate of benzene exiting the overhead product of the first column = Ex: 1.50E mol/hr

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Chemical Process Calculations

2.17.8: Making orange juice concentrate.

Maximus and Theodora are optimizing a steady state processing making orange juice concentrate. A stream of oranges (0) and a stream of water (W, H₂O) enter a juicing machine. The exit stream from the juicing machine contains 55.8 kg/hr orange juice (OJ, MW = 108), 21.3 kg/hr pulp solids (PS), and 43.5 kg/hr water. The exit stream from the juicing machine enters a filter. The filter removes all of the pulp solids and 20.2% of the water entering the filter as one exiting stream. The other stream exiting the filter contains water and orange juice. The water/orange juice mixture is finally sent to an evaporator to produce a concentrate stream (80.1 wt% orange juice and the balance water) and a stream of pure water. The pure water is recycled, mixed with a fresh stream of pure water, and fed into the juicing machine. Determine the following three unknowns.

Mole fraction of orange juice in the concentrate stream =Ex: 0.309

Mass flow rate of water entering the evaporator =Ex: 30.9 kg/hr

Mass flow rate of water entering the overall system =Ex: 16.8 kg/hr

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Chemical Process Calculations

2.17.9: Preheater and distillation column.

A preheater and distillation column are maintained by engineers Marcella and Julius. A stream of pure acetone (A, C3H6O) and a stream containing acetone, ethanol (E, C2H5OH), and butanol (B, C4H, OH)entering the preheater. One stream exits the preheater containing 144 mol/min butanol, some acetone,and some ethanol; the mole fractions of butanol and ethanol are 0.209 and 0.412, respectively. The stream of pure acetone entering the preheater is 2.42 times larger than the component flow rate of acetone in the other stream entering the preheater. The stream exiting the preheater enters a distillation column, and all of the entering butanol exits in the bottom product stream. The recoveries in the overhead product, which is defined and the ratio of component flow rate exiting to component flow rate entering the distillation column, of acetone and ethanol are 83.1% and 59.2%, respectively. Determine the following three unknowns.

Mass fraction of apple in the solid waste =Ex: 0.632

Total flow rate of the concentrate =Ex: 8.82kg/min

Flow rate of pure water entering the overall system =Ex: 8.95kg/min

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Chemical Process Calculations

Engineers Sophia and Giles are modifying a process to make concentrated apple cider starting from a slurry - a slurry is a mixture of solids in a liquid that can normally be pumped. A slurry made with apple shaving a mass fraction of 0.422 and the balance water is fed to a juicer at a rate of 26.2 kg/min. Seventy percent of the apples entering the juicer leave as part of the solid waste stream (containing apples and water). The primary product from the juicer is cider (35.3 wt% apples and 64.7 wt% water). The cider is sent to an evaporator where concentrate - apple concentration increases to 51.5 wt% - is produced along with a stream of pure water that is recycled. The pure water stream leaving the evaporator is mixed with fresh water entering the process. The combined water stream mixes with pristine apples entering the process to create the slurry. Determine the following three unknowns.

Mass fraction of apple in the solid waste =
Ex: 0.632

Total flow rate of the concentrate = Ex: 8.82 kg/min

Flow rate of pure water entering the overall system = Ex: 8.95kg/min

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Circuits

Problem 3 For the following circuit, use nodal analysis to write the FOUR equations in standard form. DO NOT SOLVE. You must identify any quasi-supernodes, supernodes, auxiliary equations, and remove dependent variables. Your final equations may only have V₁, V2, V3 and/or V4 as unknowns. Put your final equations in standard form in the box provided.

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Circuits

Problem 2 For the following circuit, write the FOUR mesh equations in standard form. DO NOT SOLVE. You must identify any super meshes, auxiliary equations, and re-move all dependent variables. Your equations may only have 11,12,13 and/or 14 as unknowns. Put your final equations in standard form in the box provided.

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Circuits

Problem 1.1 Determine Reg in Ohms at the (a,b) terminals for the following circuit. Round your answer to the nearest single digit decimal place (tenths).

Problem 1.2 Determine the voltage V, in Volts for the following circuit. Round your answer to the nearest single digit decimal place (tenths).

Problem 1.3 Determine the current I, in Amps for the following circuit. Round your answer to the nearest single digit decimal place (tenths).

Problem 1.4 Determine the power, P3n, delivered to the 302 resistor in Watts for the following circuit.Round your answer to the nearest single digit decimal place (tenths).

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Modern Physics

1A cruiser moves away from the planet Hoth at a speed of 0.5c. A frigate follows, catching up at a speed of 0.25c as viewed from the cruiser. With what speed does the frigate appear to be moving according to observers on the planet? You should use the relativistic velocity transformation, clearly defining all the parameters used.

u^{\prime}=\frac{u-v}{1-\frac{u v}{c^{2}}}

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Linear Algebra

In an election campaign, the popularity, B, as a percent of voters, of the governing Blue party can be modelled by a function of time, t, in days throughout the campaign as B(t) = 40 - 0.5t. The popularity, R(t), of the opposing Red party can be modelled by a composite function of B(t),R(B(t)) = 20 + 0.75[40 – B(t)].

Graph B(t) and describe the trend.

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