A Railroad Tunnel Is Shaped Like a Semi-Ellipse $\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 625 } = 1$

question 337

Multiple Choice

A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 25 ft and the vertical clearance must be 20 ft at a point 18 ft from the center. Find an equation for the ellipse.

• A) \(\frac { x ^ { 2 } } { 324 } + \frac { y ^ { 2 } } { 625 } = 1\)
• B) \(\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 625 } = 1\)
• C) \(\frac { x ^ { 2 } } { 900 } + \frac { y ^ { 2 } } { 400 } = 1\)
• D) \(\frac { x ^ { 2 } } { 625 } + \frac { y ^ { 2 } } { 900 } = 1\)

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Definitions:

Standard Deviation

A measure of the dispersion or spread of data points in a data set, indicating how much variation exists from the average.

Standard Deviation

A measure of the dispersion or spread of a set of data points from their mean, indicating the variability within the dataset.

Budget Line

A diagram showing all imaginable combinations of two products that can be bought given a fixed budget at unchanged price points.

Expected Rate

The forecasted or anticipated rate of return on an investment or the future rate of interest on a loan.