If f(x) = 3x2 – 4 and g(x) = 2x – 6, what is g(f(2))?
O-16
o -2
O 8
0 10

The last option, 10 is correct

Step-by-step explanation:

f(x) = 3x^2 - 4

f(2) = 3(2)^2 - 4

f(2) = 12 - 4

f(2) = 8

g(x) = 2x - 6

g(8) = 2(8) - 6

g(8) = 16 - 6

g(8) = 10

This means that g(f(2)) is equal to 10

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.

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5