BRIDGE CONSTRUCTION Your team is working for the transport authorities of a certain city. You have to
analyze two construction projects for a new bridge over the river in said city. The
spacing between the bridge supports needs to be 1050 feet and the height at the center of the arch
350 cakes. One company has suggested that the structure be in the shape of a parabola; other
company suggests a semi-ellipse. The engineering team will determine the relative resistances of
the two projects; your job is to find if there is any difference in the widths of the
channel.
An empty oil tanker needs a clearance of 280 feet to pass under the bridge.
You must find the width of the channel in each of the proposals.
1. To determine the equation of a parabola with these characteristics, first place the
parabola on coordinate axes in a convenient position and draw it.
2. What is the equation of the parabola? (If you use decimal point in the equation, approximate to
six decimal places. If you use fractions, your answer will be more exact.)
3. If the shape of the satellite dish supports, how wide will the channel it will pass through
the oil tanker?
4. To determine the equation of a semi-ellipse with these characteristics, place the
semi-ellipse on coordinate axes in a convenient position and draw it.
5. What is the equation of the ellipse? How wide will the canal need to be for the
Petroleum ship?
6. Now that you know which of the two alternatives provides the widest channel, consider other
factors. His department is also in charge of verifying the depth of the channel, the
amount of river traffic and other details. For example, if there was a flood in the river and
the water level will rise 10 feet, how would free space be affected? Take a decision
about which project you think would be best as far as your department is concerned and
explain your decision.

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

The amount spent on food and drink by 20 customers is shown below what is the modal amount spent ?

The area of a rectangle is 10 cm^2. one side of the rectangle is x cm. express the perimeter of the rectangle in terms of x and show that this rectangle cannot have a perimeter of 12 cm. the perimeter of the rectangle in terms of x is __ cm