A rectangular prism with a volume of 45 cubic centimeters and a height of 3 cm has a base with an area of
square centimeters.

Area: 15cm^2

Base: 5cm

Step-by-step explanation:

The volume of a Rectangular Prism is given as:

V= wlh

Where W = Base

L = Length

H= Height

From the question:

The Volume V = 45cm^3

The Height H = 3

But, Area = Length * Width

Therefore :

Volume V = Area * Height

45 = A * 3

A = 45/3

A= 15cm^2

Solving for Base:

Area = height * Base

15 = 3 * Base

Base = 15/3

Base = 5cm

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}