An indoor water park has two giant buckets that slowly fill with 1000 gallons of water before dumping it on the people below. one bucket dumps water every 16 minutes. the other bucket dumps water every 14 minutes. it is currently 3: 25 p. m. and both buckets dumped water 5 minutes ago. find the next two times that both buckets dump water at the same time.
first time: p. m

The next two times that both buckets dump water at the same time are 5:12 P.M. and 7:04 P.M.

Step-by-step explanation:

To find out the next two times both buckets dump water at the same time we first must find the least common multiple (LCM) between the period it takes for each bucked to dump water, that is, LCM (14,16).

The numbers can be decomposed as 2 x 7 and 2 x 8, therefore, the LCM is:

Since the last time that both buckets dumped water at the same time was 3:20 P.M., to discover when they will simultaneously dump water again we should add 112 minutes(1 h 12min) to the last time it happened:

The same can be done to find next time that it will happen  again:

The next two times that both buckets dump water at the same time are 5:12 P.M. and 7:04 P.M.

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.

the answer is 21%.