A retail store sells two types of shoes, sneakers and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more that $2,000 on inventory of the shoes. Let x= the number of sneakers in stock, and y=the number of sandals in stock. Write an equation to show the profit she will make on sneakers and sandals. P = [answer0]

The equation that shows the profit: P = 2x + 3y

Step-by-step explanation:

The number of sneaker = x

The number of sandals = y

Cost of sneaker = 8 dollars.

Cost of sandals = 14 dollars.

Selling price of sneaker = $10

Selling price of sandals = $17

Total revenue = $10x + $17y

Total cost  = $8x + $14y

Profit (P)  =  Total revenue  - Total cost.

Profit = ($10x + $17y) – ($8x + $14y)

P = 10x +17y – 8x – 14y

P = 2x + 3y

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.