Eva is short on frosting! She works in a bakery and has 12 cakes to frost, but she is short 418 cups on the amount of frosting required. She decides that she will spread the frosting she has among the 12 cakes. She makes a sign for the cakes and names them by the value that represents the amount of frosting on each cake compared to the amount it should have. What does the sign say?

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.

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

h/o/e/s mad

step-by-step explanation:

si si si