91Ó°ÊÓ

For what negative values of \(x\) will \(x^{18}\) be greater than \(x^{20} ?\)

For what positive values of \(x\) will \(x^{-18}\) be greater than \(x^{-20} ?\)

The sixth power of 2 is 64 ; that is \(, 2^{6}=64\) a. Write at least five other expressions, using a single base and a single exponent, that are equivalent to 64. b. Write the number 64 using scientific notation.

Simplify each radical expression. If it is already simplified, say so. $$ \frac{\sqrt{20}+\sqrt{80}}{\sqrt{20}} $$

Simplify each radical expression. If it is already simplified, say so. Challenge \(\sqrt{x+2}+\sqrt{4 x+8}\)

Rewrite each expression using a single base and a single exponent. $$(-3)^{81} \cdot(-3)^{141}$$

Sports A popular cliff for divers has a height of 18 meters from the water's surface. Once a diver has left the cliff, the height in meters of the diver, \(h\) , after \(t\) seconds can be approximated with this equation: $$h=18-4.9 t^{2}$$ a. Create a table of heights for several values of \(t\) . When you choose values for your table, think about what values would make sense in this situation. b. Use your table to sketch a graph of the relationship between height and time. c. Use your graph to predict how long it will take a diver to reach the halfway point of the dive. d. Use your graph to predict how long it will take a diver to hit the surface of the water.

Rewrite each expression as simply as you can. $$m^{-3} \cdot m^{4} \cdot b^{7}$$

Prove that each number is rational by finding a pair of integers whose ratio, or quotient, is equal to the number. $$ 3.56 $$

A particular tennis tournament begins with 64 players. If a player loses a single match, he or she is knocked out of the tournament. After one round, only 32 players remain; after two rounds, only 16 remain; and so on. Six students have conjectured a formula to describe the number of players remaining, \(p,\) after \(r\) rounds. Which rule or rules are correct? For each rule you think is correct, show how you know. \(\bullet\) Terrill: \(p=\frac{64}{2^{r}}\) \(\bullet\) Mi-Yung: \(p=64 \cdot 2^{-r}\) \(\bullet\) Antonia: \(p=64 \cdot \frac{1}{2^{r}}\) \(\bullet\) Peter: \(p=64 \cdot\left(\frac{1}{2}\right)^{r}\) \(\bullet\) Damon: \(p=64 \cdot 0.5^{r}\) \(\bullet\) Tamika: \(p=64 \cdot(-2)^{r}\)