What is the total surface area of a right rectangular prism with a base of 2 cm by 3 cm and a height of 6 cm?

The total surface area = 72 cm²

Step-by-step explanation:

∵ The dimensions of the rectangular prism are 2 , 3 and 6

∵ The prism has 2 bases shaped rectangle with dimensions 2 and 3

and four side faces each two has same dimensions 2 , 6 and 3 , 6

∴ The total surface are = 2(2 × 3) + 2(2 × 6) +2(3 × 6)

                                      = 12 + 24 + 36 = 72 cm²

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}