The first term of an arithmetic sequence is -4. the 8th term is 10. what is the common difference?

  2

Step-by-step explanation:

The general term of an arithmetic sequence is given by the explicit formula ...

  an = a1 +d(n -1)

The first term is a1 = -4, and the 8th term is a8 = 10. Using these numbers in the formula, we find ...

  a8 = a1 +d(8 -1) . . . . put n=8 into the formula

  10 = -4 + 7d . . . . . . . fill in the other known values

  14 = 7d . . . . . . . . . . . add 4

  2 = d  . . . . . . . . . . . . . divide by 7

The common difference is 2.

You may have noticed that the difference between the first and eighth terms is 8-1 = 7 times the common difference. And, our solution is ...

  d = (10 -(-4))/7 = 2

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.

probably .5

i can on others if necessary.