The ratio of brown tiles to white tiles in Mrs. Harris kitchen in 4 to 5. There are 180 white tiles in the kitchen. What is the total number of tiles in mrs. Harris kitchen

405

Step-by-step explanation:

Don't be confused about setting up the proportion. White has to go with white which is 4 and brown goes with 5.

The total is 9.

so proportion will look like this.

4/9 = 180/x          Cross Multiply

Before I solve this, notice that the white data is on top of the fraction, and the total is on the bottom of the fraction on either side of the proportion.

4x = 180 * 9

4x = 1620

x = 1620 / 4

x = 4 0 5

Notice that the brown is going to be bigger than the white but not by much

White                            180

Brown       405 - 180 = 225

Total                              405

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.

college