Homework Answers
Lets name the nodes as follows
Our approach is to equal 
for each node 
.
NODE 1
.
NODE 2
.
NODE 3
NODE 4
.
With node 4 we have
. Replacing it in node 3 we get 
or 
. Replacing in node 1,
and 
. Finally, using the equation for node 2 we have 
and 
.
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8) The flow of traffic in vehicles per hour is show in the diagram. Solve the...
The figure shows the flow of traffic (in vehicles per hour) through a network of streets....
The figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a = 100 and b = 400.) X1 a X4 (a) Solve this system for Xi, i = 1, 2, 3, 4. (If the system has an infinite number of solutions, express x1, x2, x3, and x4 in terms of the parameter t.) (x1, x2, x3, x4) = (b) Find the traffic flow when X4 = 0. (X1, X2, X3, X4) (c) Find...
The figure shows the flow of traffic (in vehicles per hour) through a network of streets....
The figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a = 100 and 400.) b XI a 33 X4 (a) Solve this system for Xi 1, 2, 3, 4. (If the system has an infinite number of solutions, express X1, X2, Xy, and x4 in terms of the parameter t.) (X1, X2, X3, X4) (b) Find the traffic flow when X4 = 0. (X1, X2, X3, X4) = (c) Find the traffic...
The figure shows the flow of traffic (in vehicles per hour) through a network of streets....
The figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a 300 and b 50.ג x1 X2 14 (a) Solve this system for xi, 1, 2, 3, 4. (If the system has an infinite number of solutions, express x1, x2, x3, and x4 in terms of the param eter t.) (x1, X2, X3, X4)-+100,t- 300,t400,t x (b) Find the traffic flow when x40 (xi, x2, x3, xa) - (c) Find the traffic flow...
c. Estimate the traffic flow in vehicles per hour at a speed of 39 miles per...
c. Estimate the traffic flow in vehicles per
hour at a speed of 39 miles per hour (to 2 decimals).
The estimated value is = ____ (to 2 decimals)
99% Confidence interval = ( , ) (to 2 decimals)
99% Prediction interval = ( , ) (to 2 decimals)
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. ŷ = bo + b12+b222 where y=traffic flow in vehicles per hour I...
A roadworks site is set up on a road carrying a flow of 1200 vehicles per...
A roadworks site is set up on a road carrying a flow of 1200 vehicles per hour at a speed of 60 kilometres per hour. The roadworks restricts the capacity of the road to half of the arrival flow, causing a queue to build up of vehicles that travel at a speed of 10 kilometres per hour. a) Identify the flow and density conditions of the arriving traffic stream, and of the slow-moving queue of vehicles b) Sketch these two...
The accompanying figure shows a network of one-way streets with traffic flowing in the directions...
The accompanying figure shows a network of one-way streets with traffic flowing in the directions indicated. The flow rates along the streets are measured as the average number of vehicles per hour. 300 800 275 300 700 BI 200 250 25 (a) Set up a linear system whose solution provides the unknown flow rates. С X1- X2 - 25 x2 x3 --500 x3 + x4 = 450 +x4 = 25 С X1.x2 - 25 --500 x2X3 x3 +x4 = 450...
Problem 4: Suppose that the movement of rush-hour traffic on a typical expresswa be modeled using the differential equation du du where u(x) is the density of cars (vehicles per mile), and a is dista...
Problem 4: Suppose that the movement of rush-hour traffic on a typical expresswa be modeled using the differential equation du du where u(x) is the density of cars (vehicles per mile), and a is distance miles) in the direction of traffic flow. We w to the boundary conditions ant to solve this equation subject u(0) 300, u(5) 400. a) Use second-order accurate, central-difference approximations to discretize the differential equation and write down the finite-difference equation for a typical point zi...
ı d. Is points) The tollowing figure d hour (vph) describes a flow of traffic, with the units bei...
ı d. Is points) The tollowing figure d hour (vph) describes a flow of traffic, with the units being vehicles per (a) Describe a system of linear tras The total time it takes the vehicles to travel any stretch of road is proportio traffic along that stretch. For exam to travel any stretch of road is proportional to the AB is k along that stretch. For example, the total time it takes i vehicles to travere minutes. Ass veiles to...
A highway department is studying the relationship between traffic flow and speed. The following m...
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized where y traffic flow in vehicles per hour x vehicle speed in miles per hour The following data were collected during rush hour for six highways leading out of the city Traffic Flow (y) 1,256 1,330 1,226 1,335 1,350 1,125 Vehicle Speed (x) 35 35 50 25 Enter negative values as negative, if necessary a. Show the estimated regression equation (to 3...
The following is a random sample of n = 90 undergraduate students' annual textbook expense. 610...
The following is a random sample of n = 90 undergraduate students' annual textbook expense. 610 600 300 420 520 470 430 520 400 370 730 480 450 500 650 370 540 330 690 550 450 450 750 750 660 700 300 770 760 390 680 450 590 630 530 700 580 390 330 320 350 490 310 320 780 590 370 470 760 550 630 450 640 620 520 440 720 660 440 770 380 450 800 720 370...
The figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a = 100 and b = 400.) X1 a X4 (a) Solve this system for Xi, i = 1, 2, 3, 4. (If the system has an infinite number of solutions, express x1, x2, x3, and x4 in terms of the parameter t.) (x1, x2, x3, x4) = (b) Find the traffic flow when X4 = 0. (X1, X2, X3, X4) (c) Find...
The figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a = 100 and 400.) b XI a 33 X4 (a) Solve this system for Xi 1, 2, 3, 4. (If the system has an infinite number of solutions, express X1, X2, Xy, and x4 in terms of the parameter t.) (X1, X2, X3, X4) (b) Find the traffic flow when X4 = 0. (X1, X2, X3, X4) = (c) Find the traffic...
The figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a 300 and b 50.ג x1 X2 14 (a) Solve this system for xi, 1, 2, 3, 4. (If the system has an infinite number of solutions, express x1, x2, x3, and x4 in terms of the param eter t.) (x1, X2, X3, X4)-+100,t- 300,t400,t x (b) Find the traffic flow when x40 (xi, x2, x3, xa) - (c) Find the traffic flow...
c. Estimate the traffic flow in vehicles per
hour at a speed of 39 miles per hour (to 2 decimals).
The estimated value is = ____ (to 2 decimals)
99% Confidence interval = ( , ) (to 2 decimals)
99% Prediction interval = ( , ) (to 2 decimals)
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. ŷ = bo + b12+b222 where y=traffic flow in vehicles per hour I...
A roadworks site is set up on a road carrying a flow of 1200 vehicles per hour at a speed of 60 kilometres per hour. The roadworks restricts the capacity of the road to half of the arrival flow, causing a queue to build up of vehicles that travel at a speed of 10 kilometres per hour. a) Identify the flow and density conditions of the arriving traffic stream, and of the slow-moving queue of vehicles b) Sketch these two...
The accompanying figure shows a network of one-way streets with traffic flowing in the directions indicated. The flow rates along the streets are measured as the average number of vehicles per hour. 300 800 275 300 700 BI 200 250 25 (a) Set up a linear system whose solution provides the unknown flow rates. С X1- X2 - 25 x2 x3 --500 x3 + x4 = 450 +x4 = 25 С X1.x2 - 25 --500 x2X3 x3 +x4 = 450...
Problem 4: Suppose that the movement of rush-hour traffic on a typical expresswa be modeled using the differential equation du du where u(x) is the density of cars (vehicles per mile), and a is distance miles) in the direction of traffic flow. We w to the boundary conditions ant to solve this equation subject u(0) 300, u(5) 400. a) Use second-order accurate, central-difference approximations to discretize the differential equation and write down the finite-difference equation for a typical point zi...
ı d. Is points) The tollowing figure d hour (vph) describes a flow of traffic, with the units being vehicles per (a) Describe a system of linear tras The total time it takes the vehicles to travel any stretch of road is proportio traffic along that stretch. For exam to travel any stretch of road is proportional to the AB is k along that stretch. For example, the total time it takes i vehicles to travere minutes. Ass veiles to...
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized where y traffic flow in vehicles per hour x vehicle speed in miles per hour The following data were collected during rush hour for six highways leading out of the city Traffic Flow (y) 1,256 1,330 1,226 1,335 1,350 1,125 Vehicle Speed (x) 35 35 50 25 Enter negative values as negative, if necessary a. Show the estimated regression equation (to 3...
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