Each year, Alex gets a raise of 8% plus an additional $100. In 2011, Alex’s annual salary was $47,563.84. (a) What will Alex’s salary be in 2013? (Round your answer to the nearest cent.) (b) What was Alex’s salary in 2009? (c) From the two options below, which deal will give Alex the higher salary after 4 years? • Take the salary scale from part b.
• In January 2010, get a raise of 8%, and in January of 2011, get a raise of 8.15%, and in the next two years, get raises of 8.30% and 8.45%, respectively.

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.

where is the figure