Students are practicing their dance for the school play. They need to start in position 1 located at (3,5) then go to position 2 at (1, 2), to position 3 at (-1,-1), and finally to position 4. Describe the
translation between each position, and give the location of the 4th position.
А
(x, y) = (x + 2, y + 3); (1,2)
B
(x, y) → (x - 2,7 – 3); (1, 2)
(x, y) → (x + 2, Y.- 3);(-3,-4)
(x, y) → (x-2,7-3);(-3,-4)

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}

4a. is 3 miles every hour

4b. is 1/3 of an hour per mile

step-by-step explanation: