Let A be the set of all strings of 0's, 1's, and 2's that have length 4 and for which the sum of the characters in the string is less than or equal to 2. Define a relation R on A as follows. For every s, t ∈ A, s R t ⇔ the sum of the characters of s equals the sum of the characters of t. Which of the following is true for R? (Select all that apply.) R is reflexive. R is symmetric. R is transitive. R is neither reflexive, symmetric, nor transitive.

Reflective

Symmetric

Transitive

Step-by-step explanation:

A is reflexive: Since the relation is based on the sum of characters in a string, s=s, so sAs.

A is symmetric: Suppose s and t are strings. if sAt, then s and t have the same sum of their characters, so tAs.

A is transitive: Suppose s,t and r are strings. if sAt, and tAr, then since s and t have the same sum, and t and r have the same sum, s and r have the same sum. So sAr.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.