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Use the following to prepare for your exploration meeting:

a.a.

b.

c.

d. e.

f. The velocity *v* in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop *h* in feet and the velocity of the coaster at the top of the hill by the formula:

g. The speed of sound in air *c* is determined by the temperature of the air. The speed in meters per second is given by

,

where *t* is the temperature of the air in degrees Celsius.

Be prepared to answer the following in your exploration meeting.

1. Demonstrate how to solve or simplify each equation or expression. Be sure to explain each step.

2. Refer to part f. Can that expression be simplified to ? Justify your answer.

3. If you knew the value of *c* in part g, show how you would find the value of *t*. Be sure to explain each step.

4. One of the equations above has a cubic root. Is the process for solving for a cubic root the same as solving for a square root? Explain your reasoning.

5. How many expressions used imaginary numbers? Was there any way to simplify or solve those expressions or equations without using imaginary numbers? Explain.

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