Use pascal's triangle to expand the binomial.
(s+3v)^5

a. s^5 - 5s^4 + 10s^3v^2+5sv^4 - v^5
b. s^5 + 15s^4v +90s^3v^2 + 270s^2v^3 + 405sv^4 + 243v^5
c. s^5 + 45s^4v+270s^3v^2+810s^2v^3+1,215sv^ 4 + 729v^5
d. s^5 + 15s^4 + 90s^3 + 270s^2 + 405s + 243

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.

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there is no question content here, but you for the free points! : d