8. A novel has 14 times as many pages as a short story. The combined number of pages in the books is 390 pages. How many pages are in each book?

The short story have 26 pages

The novel's pages is  364

Step-by-step explanation:

Step one:

given data

let the short story have x pages

so that the novel's pages will be 14x

the combined pages for novel and short story is =390 pages

Required

the individual number of pages

14x+x=390

15x=390

divide both sides by 15

x=26

the short story have 26 pages

the novel's pages will be 14(26)= 364

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.

47 - 90 = 43

43 - 180 = x

x = 137