PreCalculus
Find the solutions of each equation on the interval [0, 2π).
1.
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2. The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady.
Country Population in 2000 Growth Rate
Australia 19,169,000 0.6%
China 1,261,832,000 0.9%
Mexico 100,350,000 1.8%
Zaire 51,965,000 3.1%
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3. Solve .
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Estimate and classify the critical points for the graph of the function.
4.
5. Astronomers classify stars according to their brightness by assigning them a stellar “magnitude.” The higher the magnitude the dimmer the star. The dimmest stars visible to the naked eye have stellar magnitudes of 6. The table below shows the relative brightness of different stellar magnitudes.
Stellar Magnitude 1 2 3 4 5 6
Relative Brightness 100 40 16 6.3 2.5 1
a. Find an equation that gives the relative brightness in terms of stellar magnitude.
b. Use this equation to find the relative brightness of a star with magnitude 9.
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6. A restaurant offers a lunch special in which a customer can select from one of the 7 appetizers, one of the 10 entrees, and one of the 6 desserts. How many different lunch specials are possible?
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Divide using long division.
7.
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Condense each expression.
8.
9. A gear of radius 6.1 cm turns at 11 revolutions per second. What is the linear velocity of the gear in meters per second?
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