# Functions and Coordinate Geometry

Functions and Coordinate Geometry -

(1) Find an equation of the line having the given slope and containing the given point

m= , (6,-8)

(2) Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b

(7,8); x+7y=5

...

...

(6) The table lists data regarding the average salaries of several professional athletes in the years 1991 and 2001.

a) use the data points to find a linear function that's fits the data

b) use the function to predict the average salary in 2005 and 2010

(7) In 1920, the record for a certain race was45.6 sec. In 1970, it was 45.1 sec. let R(t)= the record in the race and t= the number of years since 1920.

Questions are in the attached file.

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#### Solution Summary

All the 7 questions solved step-by-step.

Geometry Questions

1. Consider the graph of y = tan x.

(a) How does it show that the tangent of 90 degrees is undefined?

(b) What are other undefined x values?

(c) What is the value of the tangent of angles that are close to 90 degrees (say 89.9 degrees and 90.01 degrees)?

(d) How does the graph show this?

2. A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius. The formula is N(P) = 6066 - 31 cos 2P, where P is the latitude in degrees.

(a) Using the Library and other course resources, find the exact latitude (to 4 decimal places) of where you live, used to live, work, or used to work (include the zip code).

(b) Using the latitude found in part a and the formula N(P), find the length of a nautical mile to the nearest foot at that location.

(c) Next, use the formula N(P) to find the latitude where the nautical mile is 6051 feet.

(d) Name two cities in the Northern Hemisphere and two in the Southern that are close to the latitude found in part c.

3. When graphed using polar coordinates, the center of a regular nonagon is at the origin and one vertex is at (6, 0 degrees) or (6, 0 radians). Find the polar coordinates of the other vertices in both degrees and radians.

Click option 1 which is http://www.mathematicshelpcentral.com/graph_paper.htm

or option 2 http://www.richardmartino.com/math/polar.htm

for polar coordinate graph paper

Reference:

Bittinger, M. L., & Beecher, J. A. (2000). Trigonometry update. Reading, MA: Addison Wesley.

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