In a paint factory, an old conveyer line has filled 50 barrels of paint, and is filling more at a rate of 2 barrels per minute. A worker just switched on a newer line that can fill 12 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled?

60 barrels

Step-by-step explanation:

y = # of barrels; x = minutes

worker: y = 12x

old line: y = 2x + 50

12x = 2x + 50

10x = 50

x = 5

y = 12(5) = 60

y = 2(5) + 50 = 60

60 barrels

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.

john got lost so he didn't know what to do and it was crazy because he didn't except it

step-by-step explanation:

123123 step byt step