Chapter 9.1, Problem 50E

a.

To determine

To draw: the polar plane.

Explanation of Solution

Given information:

The region is $-\frac{\pi }{3}\le \theta \le \frac{\pi }{3}\text{ and }0.25\le r\le 3$ .

Graph: to draw the graph, use the polar coordinates,

The polar coordinates can be

  $\left(0.25,-\frac{\pi }{3}\right),\left(1,-\frac{\pi }{3}\right),\left(3,-\frac{\pi }{3}\right),\left(2,-\frac{\pi }{3}\right),\left(0.25,\frac{\pi }{3}\right),\left(1,\frac{\pi }{3}\right),\left(3,\frac{\pi }{3}\right),\left(2,\frac{\pi }{3}\right)$

Thus, by using the above polar coordinates the graph can be obtained as:

  

Interpretation: from the above graph it can be observed that the graph shape is amphitheater.

b.

To determine

To find: the number of seat if each person has $6$ square feet of space.

Answer to Problem 50E

The number of seats is $300$ .

Explanation of Solution

Given information:

The region is $-\frac{\pi }{3}\le \theta \le \frac{\pi }{3}\text{ and }0.25\le r\le 3$ .

Calculation: form the above graph it can be observed that if each person has $6$ square feet of space, the number of seats $300$ .