Gary has guitar lessons every 5 days and band practice every 4 days his first band practice is in 4 days and his first guitar lessons and band practice on the same day explain how you know

20 days

Step-by-step explanation:

Gary has guitar lessons every 5 days

Gary band practice every 4 days

Gary first guitar lessons and band practice on the same day.

Next day when both practice on same day should be multiple of 4 and 5.

Least common multiple of 4 and 5 ,

4 = 4, 8, 12, 16, 20, 24,

5 = 5, 10, 15, 20, 25,

Common multiple in both number is 20.

After 20 days he will got for guitar lesson and band practice same day.  

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.