A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap.

Part A
Which equation relates the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.
A. b = 13g
B. b = 12g
C. b = 23g
D. b = 32g

Part B
Which equation relates the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.
A. p = 13b
B. p = 12b
C. p = 23b
D. p = 34b

Part A = B.

Part B = A.

Step-by-step explanation:

for the points! : )

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}