An office and apartment building is made up of modules. Each module is a rectangular prism. The building has 150 modules, and is 15 stories high. If all of the modules were divided evenly among the number of stories, how many modules would be on each floor? How many different rectangular prisms could be made from that number? If all of the modules were divided evenly there would be modules on each floor. different rectangular prisms could be made from the number of modules on each floor: × 1 × 1 and 2 × × 1.

Part 1. 10 modules per floor

Part 2. Two different rectangular prism

Step-by-step explanation:

Let

x > the number of modules

y ---> the number of stories

we have

x=150\ modules\\y=15\ stories

Divide the number of modules by the number of stories

so

\frac{x}{y}=\frac{150}{15}=10\ \frac{modules}{floor}

7

step-by-step explanation:

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}