Question

We define two numerical operations labeled T and R.
The effect of T is to add 1 to a number. For example, if we apply the operation T to the number 2 three times in a row, we obtain 3, then 4, then 5.
The effect of R is to find the negative reciprocal of a number. For example, if we apply the operation R to 2 we obtain – ½, and if we apply the operation R to -3/2 we obtain 2/3. Note that R can never be applied to the number 0.
The operations T and R can be combined. For example, we can turn 0 into 2/5 by successively applying the operations T, T, T, R, T, T, R, T:
0 ---T ---> 1 ---T---> 2 ---T ---> 3 ---R---> -1/3 ---T ---> 2/3 ---T ---> 5/3 ---R ---> -3/5 ---T ---> 2/5.
a. Starting with 2, list the numbers produced by successively applying the operations
T, R, R, T, R, T, R, T, R.

b. Find a sequence of operations which turns ¾ into 2/3
c. Find a sequence of operations which turns 3 into 0.
d. Find a sequence of 20 operations that turn 7 into 0.

Please help

Answer 1

a. 3 , -1/3 , 3 , 4 , -1/4 , 3/4 , -4/3 , -1/3 , 3

b. R , T , T

c. R , T , R , T , T , R , T , T

d. R , T , R , T , T , R , T , T , R , T , T , R , T , T , R , T , T , R , T , T

Answer 2

scott is correct although I don't think B is.

Answer 3

ohhh nevermind, I understand that scott was doing. my bad lol

Answer 4

This is in a comp booklet, why did you post this???

Answer 5

how does a go from -1/4 to 3/4??

Answer 6

ohh i get it know tho