Ralph is 3 times as old as sara. in 6 years, ralph will be only twice as old as sara will be then. find ralph's age now. ralph's age is a)6 b)12 c)18 d)24

C)18

Step-by-step explanation:

Let Sara present age = x years.

According to question Ralph present  age =3x

Sara age after 6 years =x+6.

Ralph age after 6 years =3x+6.

After 6 years Ralph will be only twice as old as Sara will be then.

3x+6=2(x+6)

Solving for x:

3x+6=2x+12

3x-2x=12-6

x=6.

Ralph present age = 3x=3(6)= 18 years.

Option C.

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}

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values