My math final is monday and I've been up studying this weekend. I am pretty sure I've got most of my material down but I do have 3 questions I need the answers too. Out of 30 questions on a practice test I'm havign trouble with these three so I don't think I'm doing ot bad. Here they are with linked pictures for the diagrams I typed them out as best I could. Any help is much appreciated, thanks!
Question 1. An arch of a bridge is semi-elliptical, with major axis horizontal. The base of the arch is 30 feet across, and the highest part of the arch is 10 feet above the horizontal roadway.
a) Give the equation of the ellipse in standard form b) Find the height of the arch ten feet from the center of the horizontal roadway.
Here is link to pic of diagram for that problem...
Question 2. A satellite antenna dish has the shape of a paraboloid that is 10 feet across at the open end and is 3 feet deep. At what distance from the center of the dish should the reciever be placed to recieve the greatest intensity of sound waves?
Question 3. Shown in the figure is a system of 4 one way streets leading into the center of a city. The numbers in the figure denote the average number of vehicles per hour that travel in the directions shown. A toal of 300 vehicles enter the area and 300 vehicles leave the area every hour.
Signals at intersections A,B,C and D are to be timed in order to avoid congestion, and this timing will determine flow rates x1, x2, x3, and x4
a) If the number of vehicles entering an intersection per hour must equal the number of vehicles leaving the intersection per four, describe the traffic flow rates at each intersection with a system of equations.
b) If the signal at intersection C is timed so that x3 = 100, find x1, x2, and x4
Here is a link to the diagram for this problem...
Like I said the final is monday so any help is much appreciated, thanks!