Chapter 2.3, Problem 37E

To determine

To calculate:

The inequality equation in terms of the circumference of circle

Answer to Problem 37E

The inequality in the term of circumference of circle is $C>10\pi$ .

Explanation of Solution

Given information:

  $\begin{array}{l}r>5\\ r=\frac{C}{2\pi }\end{array}$

Calculation:

The inequality equation for radius of circle is given as:

  $r>5$  .. . . . (1)

Another equation of radius in terms of circumference of circle $C$ is given as:

  $r=\frac{C}{2\pi }$  .. . . . (2)

Put value of $r$ from eq. (2) in eq. (1):

  $r>5$

  $\frac{C}{2\pi }>5$  .. . . . (3)

Multiply by $2\pi$ on both sides of equation (3):

  $\begin{array}{l}\frac{C}{2\pi }>5\\ \frac{C}{2\pi }\times 2\pi >5\times 2\pi \\ C>10\pi \end{array}$

Therefore, the inequality in the term of circumference of circle is $C>10\pi$ .