Amelia is participating in a 60-mile spin-a-thon. Her spin bike keeps track of the simulated number of miles she travels. She plans to take a 15-minute break within 5 miles of riding 30 miles. Amelia spins at a constant 22 mph. You can use the table to help organize your thinking.
C. Make Sense and Persevere About how many hours will Amelia spin before she takes a break? Discuss how you could use your mathematical model to complete the spin-a-thon schedule.

i assume that by 5 you mean 5 gallons.

(20)(0.25) = 15

removing 15 gallons reduces the tank from 20 to 5.

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}

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right

they r 125, and 216

so the sequence goes 1,8,27,64,125,216