Question

city officials rope off a circular area to prepare for a concert in the park. they estimate that each person occupies 6 square feet. describe how you can use a radical inequality to determine the possible radius of the region when p people are expected to attend the concert.

Answer 1

To determine the possible radius of the circular area for a concert, a radical inequality can be used by setting up the equation πr^2 ≥ 6p, where 'r' represents the radius and 'p' represents the number of people. By solving the inequality, we can find the range of values for 'r' that can accommodate the given number of people.

Step-by-step explanation:

To determine the possible radius of the circular area, we can use a radical inequality. Let's denote the radius as 'r' and the number of people as 'p'. We know that each person occupies 6 square feet. The area of a circle is given by the formula A = πr^2. So, the total area needed for 'p' people would be 6p, since each person occupies 6 square feet. Therefore, we can set up the following inequality:

πr^2 ≥ 6p

In this inequality, the value of 'r' represents the radius of the circular area, and 'p' represents the number of people expected to attend the concert. By solving this inequality, we can find the possible range of values for 'r' that can accommodate the given number of people.

Answer 2

Step-by-step explanation:

the area of a circle is

pi×r²

r being the radius.

so, now we know that this area has to contain p people, each of them occupying 6 ft².

so, the area is 6p ft².

therefore,

6p = pi×r²

r² = 6p/pi

r = sqrt(6p/pi) ft

the actual roped-off area has to be at least that size (6p ft²), so the inequality is then

r >= sqrt(6p/pi) ft