Jordan went swimming each day of his vacation. on monday he swam for 3/4 of an hour, on tuesday he swam for 2 1/4 hours, on wednesday he swam for 1/2 of an hour, on thursday he swam for 1 3/4 of an hour, and on friday he swam 1/4 of an hour. which list shows the times in order from shortest to longest?

Friday, Wednesday, Monday, Thursday, and then Tuesday.

Step-by-step explanation:

Friday = 1/4 = 15 minutes

Wednesday = 1/2 = 30 minutes

Monday = 3/4 = 45 minutes

Thursday = 1 3/4 = 1h 45 minutes

Tuesday = 3 1/4 = 3h 15 minutes

answer:

sometimes

*i think

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}