A certain video game console uses 154 watt-hours of energy each hour. The console used 276 hours last year.

How many watt-hours of energy did the console use?

Use any method to solve this problem. You must show all your work.

Then, explain your reasoning and the steps you took to solve the problem.

42504

Step-by-step explanation:

As it uses 154 watt-hours per hour, in 276 hours, it would use 42504 as we would multiply the energy usage by the amount of hours used:

154 watt-hours = 1 hour

276 hours = 42504 watt-hours

276*154 = 42504

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.