Abasketball player scored 29 times during one game. she scored a total of 45 points, two for each two-point shot and one for each free throw. how many two-point shots did she make? how many free throws?

x = 2 point shot

y = free throw

x +y = 29

x = 29-y

2x +y = 45

2(29-y) + y = 45

58 -2y +y = 45

58-y = 45

-y = -13

y = 13

29-13 = 16

16*2 = 32

16 two pint shots and 13 free throws

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.