A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure. <IMAGE>
Notice that the curve in the figure is horizontal for an interval of time near $t=5.5$ hr. Give a plausible explanation for the horizontal line segment.

Evaluating inverse trigonometric functions Without using a calculator, evaluate the following expressions.

$\(\tan\)^{-1}\(\sqrt\)3$

Determine whether the following statements are true and give an explanation or counterexample.

$\frac{{\log }_{b}x}{{\log }_{b}y}={\log }_{b}x-{\log }_{b}y$

In each exercise, a function and an interval of its independent variable are given. The endpoints of the interval are associated with points $P$ and $Q$ on the graph of the function.

a. Sketch a graph of the function and the secant line through $P$ and $Q$.

b. Find the slope of the secant line in part (a), and interpret your answer in terms of an average rate of change over the interval. Include units in your answer.

After $t$ seconds, an object dropped from rest falls a distance $d=16t^2$, where $d$ is measured in feet and $2\(\leq{t}\]\leq{5}\)$.

Roots and powers Sketch a graph of the given pairs of functions. Be sure to draw the graphs accurately relative to each other.

y = (x)¹⸍³ and y = (x)¹⸍⁵

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure. <IMAGE>

Repeat the procedure outlined in part (a) for the secant line that passes through points $P$ and $Q$.

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure. <IMAGE>

Find the slope of the secant line that passes through points $A$ and $B$. Interpret your answer as an average rate of change over the interval $1\(\leq{t}\]\leq{3}\)$.