Solve the equation. 1/5x-1/6(x-2)=6x

The value for x is 10/179 or 0.0559 (Rounding to three decimal places)

Step-by-step explanation:

1. Let's solve for x, the following equation:

1/5x - 1/6 (x-2) = 6x

1/5x - 1/6x + 2/6 = 6x

6x - 5x + 10 = 180x (30 as the Lowest Common Denominator)

x - 180x = - 10

-179x = -10

x = 10/179

x = 10/179 or 0.0559 (Rounding to three decimal places)

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.