this arithmetic sequence is defined by the function f(n).

9, 13, 17, 21, 25,

what is the y-intercept of this function?

  y = 5

Step-by-step explanation:

The first term (a1) is 9, and the common difference (d) is 4. Then the general term is ...

  an = a1 + (n-1)·d = 9 + 4(n -1) = 4n +5

The "y-intercept" corresponds to the value when n=0. That value is ...

  a0 = 4·0 +5 = 5

The y-intercept is 5.

_____

Comment on the problem

We have computed f(n) for n=0, but we must realize that n=0 is outside the domain of the function. This function only makes sense for integer values of n that are greater than zero. The "real" answer is that the y-intercept is "undefined."

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.