Recall the formula for finding the area of a rectangle. define a
variable for the width and set up an equation to find the dimensions of a
rectangle that has an area 144 square inches, given that the length is 10
inches longer than its width.

Step-by-step explanation:

Given : The length is 10 inches longer than its width.

            Area of rectangle is 144 sq.inches

To Find : Define a  variable for the width and set up an equation to find the dimensions of a  rectangle

Solution:

Let the width be x

Since we are given that The length is 10 inches longer than its width.

So, Length of rectangle = x+10

Area of rectangle =

                             =  

We are given that Area of rectangle is 144 sq.inches

So,    

Since width cannot be negative

So, width of rectangle is 8 inches

Length of rectangle = x+10 = 8+10 = 18

Hence an equation to find the dimensions of a  rectangle that has an area 144 square inches is  

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}

1e+27

step-by-step explanation: