Mike and dena are painting a fence. if mike has done 1/3 of the job and dena has done 2/7 of the job, what fraction of the job is left to be finished?

8/21

Step-by-step explanation:

The total job is 1

Mike has done 1/3    and Dena has done 2/7 of the job   We still need to do x of the job to complete it

1/3 + 2/7+ x  = 1

We need to get a common denominator 3*7 = 21

Multiply each side by 21

21(1/3 + 2/7+ x)  = 1*21

21(1/3) + 21*(2/7)+ 21x  = 21

7+ 3*2 +21x =21

7+6+21x = 21

13+21x = 21

Subtract 13 from each side

13-13+21x=21-13

21x = 8

Divide each side by 21

21x/21 = 8/21

x = 8/21

We need to complete 8/21 of the job

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}

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3