Joe made a model of a door out of a piece of cardboard. The amount of cardboard used for the square, bottom portion of the model is shown in the diagram below. How much cardboard did he use in all to make the model? Give an approximate answer as well as an answer in terms of . What is the distance around the frame of the model? Give an approximate answer as well as an answer in terms of pi.

A 828  sq in

Step-by-step explanation:

The area of the circle is 50.24 square inches so if you add half of 50.24 to 784 you get 828.

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}

32/80  

91/140

the last one 54 doesn't go into 45. 54/100 ?

step-by-step explanation: