Solve for all solutions of the equation. x3 - 8 = 0

x3=0+8

×3=8

x=8/3

Step-by-step explanation:

x = 2, -1+i√3, −1−i√3

Step-by-step explanation:

Factoring the left side of the equation:

x^3−2^3=0

(x−2)(x^2+x⋅2+2^2)=0

(x−2)(x^2+2x+2^2)=0

(x−2)(x^2+2x+4)=0

x−2=0

x^2+2x+4=0

First solution:

x−2=0

x=2

Second and third solution:

x^2+2x+4=0

−2±√2^2−4⋅(1⋅4)/2⋅1

x=−2±2i√3/2⋅1

x=−2±2i√3/2

−2±2i√3/2  

x=−1±i√3

x=−1+i√3

x=−1−i√3

x=−1+i√3,−1−i√3

Final

x=2,−1+i√3,−1−i√3

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.

the answer is true.

step-by-step explanation: