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the last one

Step-by-step explanation:

Perpendicular lines will have one line with a positive slope and one lien with a negative slope first of all.

In the original problem, the slope was 3/4. So the line perpendicular is the reciprocal of 3/4 and it would be negative so -4/3

y = -4/3 x + 1/2

Step-by-step explanation:

y = 3/4 x - 1/2 has a slope of 3/4

The slope of the perpendicular line is the negative reciprocal of the original line's slope, which in this case is -4/3. The line that has this slope is

y = -4/3 x + 1/2

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}