1.9.PS-16 Question Help
o
4
Challenge Between 9 PM. and 6:20 AM, the water level in a swimming pool decreased by
in
9
Assuming that the water level decreased at a constant rate, how much did the water level drop
each hour?

0.0625 Inches

Step-by-step explanation:

Divide the decrease in water level by the length of the time interval.

decrease = 7/12 inches ≅ 0.583 inches

Time interval: From 11 pm to 8:20 am you have 9:20 hours = (9 + 20/60) hours ≅ 9.33 hours

So the water drops at a rate of about

0.583/9.33 inches/hour ≅ 0.0625 inches/hour

That means that each hour it drops about 0.0625 inches.

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}

7

step-by-step explanation: