Write the next three terms of the sequence:
1, 4, 16, 64,
256, 1024, 4096
Here, we can see that each term can be represented by where n starts at 0. We can then plug in n=4, 5, and 6 for the next three terms respectively to get the answer above.
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
l = length of minor arc
x = central angle
d = diameter
which essentially is the steps we took though a bit differently.
question 1 is 8, question 2 is 9, question 3 is 24
now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!
key: a=3, b=5, c=6
remember, a=3, so we plug that in to get 3+5=8
c=6, so we plug that in to get 15-6=9
b=6, so we plug it in to get 4*6=24
time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!
1, 4, 16, 64,