Julio is paid 1.4 times his hourly rate for each hour he works over 30 hours in a week. last week he worked 35 hours and earned 436.60. write and solve an equation to find julios normal hourly rate, r. explain how you know that that your answer is reasonable. show work so i can understand.

Here r represents Julio's normal hourly rate,

∵ He is paid 1.4 times his hourly rate for each hour he works over 30 hours,

If he worked for 35 hours,

Then, the charge for first 30 hours = normal hourly rate × 30

= 30r,

Also, the charges for additional 5 hours = new hourly rate × 5

= 1.4r × 5

= 7r

Hence, the total earnings = 30r + 7r

According to the question,

30r + 7r = 436.60

Which is the required equation,

By solving,

37r = 436.6

⇒ r = = 11.8,

Hence, the normal hourly rate is 11.8 per hour.

Verification :

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.