The can of peas below has a surface area of 180.64 cm^2. if the diamet3r of the can is 5 inches, find the height of the can.

Given the parameters given, no such can would exist due to it being too wide.

Step-by-step explanation:

To find the answer, use the formula for the surface area of a cylinder.

A = 2πrh + 2πr^2

Now input the known values and solve for h. First, make sure to use all the same units. Since the diameter of the can is written in inches, we'll change it to cm. The diameter would be 12.7cm, thus the radius would be 6.35cm.

180.64 = 2π(6.35)h + 2π(6.35)^2

180.64 = 40.13h + 254.83

-74.19 = 40.13h

-1.84 = h

Since the answer we get is negative, no such can exists.

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}