There are 23 animals in the barn. Some are geese and some are cows. There are 80 legs in all. How many of each animal are there?

17 cows and 6 geese

Step-by-step explanation:

1. set up two equations:

C + G = 23 (number of cows and geese = total number of animals)

4C + 2G = 80 (cows have 4 legs, geese have 2 legs and the total # of legs is 80)

2. 2(C+G)=2(23) ===> 2C + 2G = 46

3. subtract 4C + 2G = 80 and 2C + 2G = 46 to equal 2C=34, divide by 2 and C=17 (17 cows)

4. apply 17 back to the original (C + G = 23) equation to get: 17 + G = 23, subtract 17 from 23 and G=6 (6 geese)

i hope the way i explained it was clear! :)

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.