Chapter 7.2, Problem 79AYU

a.

To determine

The time T if you walk 1500 feet along the paved path and then 500 feet in the sand to the house.

b.

To determine

The time T if you walk in the sand directly toward the ocean for 500 feet and then turn left and walk along the beach for 1500 feet to the house.

c.

To determine

To express: The time T to get from the parking lot to the beach house as a function of the angle $\theta$.

d.

To determine

The time T if you walk directly from the parking lot to the house.

e.

To determine

The time T if you walk 1000 feet along the paved path and then walk directly to the house.

f.

To determine

To sketch: The graph $T\left(\theta \right)$, angle $\theta$ is T least, minimum time.

g.

To determine

To explain: Why $\tan \theta =\frac{1}{3}$ gives the smallest angle $\theta$ that is possible.