A 3 L bottle of oil costs $36 and contains 12 cups. Dinesh puts 1 cup of oil, 10 garlic gloves and 1 cup of lemon juice in each batch of hummus recipe that he makes. Dinesh makes 5 batches of hummus. What is the total cost of oil that he uses in the 5 batches of his recipe?

$15

Step-by-step explanation:

Let's start by figuring out how much 1 cup of oil costs.

12 cups of oil is 36$

Let's set up a proportion.

12/36=1/x

Cross Multiply

12x=36

Divide both sides by 12.

x=3

1 cup of oil is $3.

Dinesh makes 5 batches of hummus, and each batch requires 1 cup of oil.

5*1=5

This means he needs 5 cups of oil.

5*3=15

He used $15 worth of oil in the 5 batches of his recipe.

However, since it is impossible to buy 5/12 bottles of oil, he would have needed to spend $36.

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.