Mark is in a summer program that has these age requirements: Students must be more than 13 years old to take part in the program. Students must be 18 or older to work at the program. Let x represent Mark's age in years. Answer the questions to find out how old Mark could be. 1. Mark is old enough to take part in the program. Write an inequality using x that shows this. Write your answer in the space below. 2. However, Mark is too young to work in the program. Write an inequality using x that shows this. Write your answer in the space below. 3. Mark is old enough to take part in the program but too young to work at the program. List all the ages Mark could be. Explain how you found your answer. Write your answer in the space below.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.