Algebra question ( matrices and determinants ) 20 point

For this case we have the following system of equations:
 x + 2y - 6 = z
 3y - 2z = 7
 4 + 3x = 2y - 5z
 Rewriting the system we have:
 x + 2y - z = 6
 3y - 2z = 7
 2y - 5z - 3x = 4
 Solving the system we have:
 x = 7/4
 y = 3/2
 z = -5/4
 
 option A

Answer: 10pi

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.

Answers4.) -1/205.) -1/406.) -55/127.) -3/4