Question: a rectangular room has a 10 ft. by 8 ft. rug in the center such that the rug has the same amount of space to the wall on all 4 sides. find the amount of space between the rug and the wall if the room has an area of 288 sq. feet.

For this case we have that by definition, the area of a rectangle is given by:

Where:

w: It is the width

l: It is the length

Thus, the area of the rug is:

We know that the room has an area of. Subtracting we have:

Thus, the space between the wall and the rug is given by

The space between the wall and the rug is given by

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}

its adding 5.5 each time

step-by-step explanation: