Jonathan’s parents told him that for every 5 hours of homework or reading he does he gets three hours of video games. his friend lucas gets 30 minutes of playing time for every 1 hour of homework. if the boys spend the same amount of time doing homework and reading this week which boy gets more video game time

Jonathan

Step-by-step explanation                                                                                             30 * 5 = 150/ 60 = 2.5      2 hours and 30 minutes of playing time for every 5 hours is for Lucas. Jonathan gets 30 minutes more for every 5 hours.                                                                          

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.