The cantor set is constructed as follows. start with a closed interval [0, 1] and remove the open interval ( 1 3 , 2 3 ). that leaves the two intervals [0, 1 3 ] and [ 2 3 , 1]. remove the middle third of each of these closed intervals, leaving four intervals. continue the process of removing the middle third of each interval that remains from the previous step. the cantor set consists of the numbers that are not removed during the process. (a) show that the total length of the intervals removed is 1. (b) despite the result of part a. there are infinitely many numbers in the cantor set. list three numbers in the cantor set.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation: