Fernando built a robot to filter air and water efficiently. He expects the robot to filter more than 512 liters of air and water while using less than 9 Joules of energy.
A represents the number of minutes the robot filters air, and W represents the number of minutes the
robot filters water.
21A + 14W > 512 represents the number of minutes the robot filters air and water to filter more than
512 liters of air and water.
0.36 A + 0.6W < 9 represents the number of minutes the robot filters air and water while using less
than 9 Joules of energy.
Does the robot meet both of Fernando's expectations by filtering air for 15 minutes and filtering water for
5 minutes?

Khan Academy

The robot uses the expected amount of energy, but it doesn't filter the expected amount of air and water.

Step-by-step explanation:

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.