At a farm four employees harvest 48 pounds of food over a certain number of hours each employee works the number of hours shown

Complete question :

At a farm, four employees harvest 48 pounds of food over a certain numbers of hours. Each employee works the numbered of hours shown. Employee A: 6 hours employee B: 4 hours employee C: 6 hours employee D: 8 hours The number of pounds of food harvested by each employee is proportional to the number of hours worked. Fill in the table with the amount of food, in pounds, each employee harvested.

A = 12 lbs ;

B = 8 lbs

C = 12 lbs

D = 16 lbs

Step-by-step explanation:

Total hours worked :

(A + B + C + D)

(6 + 4 + 6 + 8) hours = 24 hours

Total pounds of food = 48 pounds

Pounds harvested per hour = 48 pounds / 24 hours = 2 pounds per hour

Amount of food harvested by each employee :

A = 6 * 2 = 12 pounds

B = 4 * 2 = 8 pounds

C = 6 * 2 = 12 pounds

D = 8 * 2 = 16 pounds

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.