It takes Natalie five hours to tar a roof. Imani can tar the same roof in ten hours. How long would it take them if they worked together? Round your answer to the nearest hundredth. A. 3.51 hours B. 2.77 hours C. 3.33 hours D.4.3 hours

C. 3.33 hours

Step-by-step explanation:

Use the algebra work equation:

= + , where tb is the time to work together, t1 is the time it takes one person, and t2 is the time it takes the other person

Plug in the values we know:

= +

= +

=

20 = 6tb

3.33 = tb

So, it would take them 3.33 hours when working together.

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}