Eli made a wooden box in the shape of a rectangular prism. the box has a length of 5 inches, a width of 3 1/2 inches, and a height of 7 inches.
part a. eli wants to paint the entire box green and give the box to his dad as a gift. what is the total area that he will paint? explain how you found your answer.
part b. can the box hold 22 cubic inches of packing peanuts? explain how you know.

Total surface area = 154 in²

Step-by-step explanation:

The prism has a total of 6 surfaces:  top and bottom, 2 sides, and 2 ends.

We have to find the area of each top, side, end, and then add these together, and then multiply the result by 2 to finish the job.

Area of top:  (5 in)(3.5 in) = 17.5 in²

Area of side:  (5 in)(7 in) = 35 in²

Area of end:  (3.5 in)(7 in) = 24.5 in²

Now add these three results together and multiply the sum by 2:

2( 17.5 in² + 35 in² + 24.5 in²) = total surface area = 154 in²

To answer the other part of this question:  find the volume of this prism:

V = length · width · ht = (5 in)(3.5 in)(7 in) = 122 in³.  

Yes, this box can definitely hold 22 in³ of packing peanuts.

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}

first one because it can't have a fraction in it

step-by-step explanation: