Final Examination in MATH 153 - Part 3 - re

Points A, B and C on the parabola have elevations of 30 m, 33 m and 25 m, respectively. Point B is between A and C and is 160 m horizontally from A and 90 m horizontally from C. Determine the horizontal distance of the highest point of the parabola from point A.

• 99.66 miles
• 101.77 miles
• 103.22 miles
• 105.12 miles

The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth.

• 93,000,000 miles
• 94,335,100 miles
• 91,450,000 miles
• 94,550,000 miles

The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 500 ft apart and 75 ft high. If the cables touch the road surface midway between towers, what is the height of the cable from the road at a point 120 feet from the center of the bridge?

• 14.4 ft
• 16.26 ft
• 17.28 ft
• 20.0 ft

When the load is uniformly distributed horizontally, the cable of a suspension bridge hangs in a parabolic arc. If the bridge is 300 ft long, the towers 60 ft high and the cable is 20 ft above the roadbed at the center, find the vertical distance from the roadbed 50 ft from the center.

• 10.57 ft
• 24.44 ft
• 30.57 ft
• 40.57 ft

A semi-ellipse and a parabola rest on the same base 80 meters wide and 22 meters high. Using the common base as x-axis, compute the difference of ordinates at points 28 meters from the center of the base.

• 4.49 m
• 4.95 m
• 5.29 m
• 5.67 m

If an automobile head light reflector is cut by plane through its axis, the section is a parabola having the light center as a focus. If the light is 15 mm from the vertex and the diameter of the light is 350 mm, calculate the depth of the headlight.

• 123.54 mm
• 250.5 mm
• 312.5 mm
• 510.4 mm

A hotel swimming pool has for its boundary a curve given by the equation: x² + y² = 2x - 4y + 31 where the units are all in meters. Find the volume of water required to fill the pool to a depth of 2.0 m.

• 117.8 m³
• 168.7 m³
• 121.5 m³
• 226.2 m³

An arch in the form of a semi-ellipse has a span of 90 m and its greatest height is 25 m. There are two vertical supports equidistant from each other and the ends of the arc. Find the height of the supports.

• 18.86 m
• 20.56
• 23.57 m
• 24.75 m

An arch 16 m has the form of parabola with a vertical axis. The length of a horizontal beam placed across the arch 10 m from the top is 70. Find the width of the arch at the bottom.

• 88.5 m
• 96.0 m
• 107.5 m
• 76.0 m

The moon has an apogee of 247,037 miles and a perigee of 222,037 miles. Assuming that the earth's radius is 3963 miles, what is the value of the eccentricity of ellipse which is form with the center of the earth at one focus and whose apogee and perigee satisfy the conditions above.

• 0.045
• 0.052
• 0.056
• 0.063